This document summarizes key concepts in topological spaces, including:
1. The definitions of a topological space, open sets, and examples of topologies.
2. Types of topological spaces such as T1-spaces, Hausdorff spaces, regular spaces, and normal spaces with examples.
3. Theorems relating neighborhoods, closures, and defining topologies.
4. Properties of topological spaces such as accumulation points, closed and open sets, and the closure of a set.
An Overview of Separation Axioms by Nearly Open Sets in Topology.IJERA Editor
Abstract: The aim of this paper is to exhibit the research on separation axioms in terms of nearly open sets viz
p-open, s-open, α-open & β-open sets. It contains the topological property carried by respective ℘ -Tk spaces (℘
= p, s, α & β; k = 0,1,2) under the suitable nearly open mappings . This paper also projects ℘ -R0 & ℘ -R1
spaces where ℘ = p, s, α & β and related properties at a glance. In general, the ℘ -symmetry of a topological
space for ℘ = p, s, α & β has been included with interesting examples & results.
This document discusses Galois theory and provides illustrations of the main theorem of Galois theory. It begins with an outline and introduction. The main theorem of Galois theory establishes a one-to-one correspondence between subgroups of the Galois group of a finite normal extension and intermediate fields. The document then provides examples illustrating this theorem for various polynomials and extensions. It concludes with problems related to Galois groups and extensions.
On some locally closed sets and spaces in Ideal Topological SpacesIJMER
This document introduces and studies the concept of δˆ s-locally closed sets in ideal topological spaces. Some key points:
- A subset A is δˆ s-locally closed if A can be written as the intersection of a δˆ s-open set and a δˆ s-closed set.
- Various properties of δˆ s-locally closed sets are introduced and characterized, including relationships to other concepts like generalized locally closed sets.
- It is shown that a subset A is δˆ s-locally closed if and only if A can be written as the intersection of a δˆ s-open set and the δˆ s-closure of A.
- Theore
In this paper we introduce a new class of sets known as
δ
ˆ
S –closed sets in ideal topological
spaces and we studied some of its basic properties and characterizations. This new class of sets lies
between –I–closed [19] sets and g–closed sets, and its unique feature is it forms topology and it is
independent of open sets.
This document provides an introduction to Galois theory and fields. It discusses how Galois theory originated from studying roots of polynomials and determining which polynomials are solvable by radicals. The document introduces some key concepts from Galois theory, including field extensions, the Galois group of a field extension, and Galois' theorem relating the solvability of a polynomial to the solvability of its Galois group. It also provides background on rings, algebras, and polynomial rings to set up the foundations of Galois theory.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In the present paper , we introduce and study the concept of gr- Ti- space (for i =0,1,2) and
obtain the characterization of gr –regular space , gr- normal space by using the notion of gr-open
sets. Further, some of their properties and results are discussed.
This document summarizes key concepts in topology related to the cluster point or limit point of a set in a topological space. It defines a cluster/limit point as a point such that every neighborhood of it intersects the set in at least one other point. Theorems establish that a set and its cluster points together form its closure, and that a set is closed if it contains all its cluster points. No finite set can have a cluster point. The union of a set's cluster points with the set of another's forms the cluster points of their union.
An Overview of Separation Axioms by Nearly Open Sets in Topology.IJERA Editor
Abstract: The aim of this paper is to exhibit the research on separation axioms in terms of nearly open sets viz
p-open, s-open, α-open & β-open sets. It contains the topological property carried by respective ℘ -Tk spaces (℘
= p, s, α & β; k = 0,1,2) under the suitable nearly open mappings . This paper also projects ℘ -R0 & ℘ -R1
spaces where ℘ = p, s, α & β and related properties at a glance. In general, the ℘ -symmetry of a topological
space for ℘ = p, s, α & β has been included with interesting examples & results.
This document discusses Galois theory and provides illustrations of the main theorem of Galois theory. It begins with an outline and introduction. The main theorem of Galois theory establishes a one-to-one correspondence between subgroups of the Galois group of a finite normal extension and intermediate fields. The document then provides examples illustrating this theorem for various polynomials and extensions. It concludes with problems related to Galois groups and extensions.
On some locally closed sets and spaces in Ideal Topological SpacesIJMER
This document introduces and studies the concept of δˆ s-locally closed sets in ideal topological spaces. Some key points:
- A subset A is δˆ s-locally closed if A can be written as the intersection of a δˆ s-open set and a δˆ s-closed set.
- Various properties of δˆ s-locally closed sets are introduced and characterized, including relationships to other concepts like generalized locally closed sets.
- It is shown that a subset A is δˆ s-locally closed if and only if A can be written as the intersection of a δˆ s-open set and the δˆ s-closure of A.
- Theore
In this paper we introduce a new class of sets known as
δ
ˆ
S –closed sets in ideal topological
spaces and we studied some of its basic properties and characterizations. This new class of sets lies
between –I–closed [19] sets and g–closed sets, and its unique feature is it forms topology and it is
independent of open sets.
This document provides an introduction to Galois theory and fields. It discusses how Galois theory originated from studying roots of polynomials and determining which polynomials are solvable by radicals. The document introduces some key concepts from Galois theory, including field extensions, the Galois group of a field extension, and Galois' theorem relating the solvability of a polynomial to the solvability of its Galois group. It also provides background on rings, algebras, and polynomial rings to set up the foundations of Galois theory.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In the present paper , we introduce and study the concept of gr- Ti- space (for i =0,1,2) and
obtain the characterization of gr –regular space , gr- normal space by using the notion of gr-open
sets. Further, some of their properties and results are discussed.
This document summarizes key concepts in topology related to the cluster point or limit point of a set in a topological space. It defines a cluster/limit point as a point such that every neighborhood of it intersects the set in at least one other point. Theorems establish that a set and its cluster points together form its closure, and that a set is closed if it contains all its cluster points. No finite set can have a cluster point. The union of a set's cluster points with the set of another's forms the cluster points of their union.
This document summarizes research on generalized β-closure spaces and β-connectedness. It defines key concepts such as β-closure functions, β-separated sets, and β-connectedness. Several important results are proven, including: (1) A set is β-connected if its subsets satisfy the Hausdorff-Lennes condition; (2) If a function between neighborhood spaces is β-continuous, the preimage of a β-connected set is β-connected; (3) The β-closure of a β-connected set is β-connected. The document establishes relationships between β-closure, β-separation, and β-connectedness in generalized closure spaces.
Some properties of gi closed sets in topological space.docxAlexander Decker
This document introduces generalized *i-closed (g*i-closed) sets in topological spaces and studies some of their properties. It defines what a g*i-closed set is and shows that every closed, i-closed, semi-closed, g-closed, gs-closed, and δg-closed set is also a g*i-closed set. However, the converses of these statements are not always true. Examples are provided to illustrate this. The relationships between g*i-closed sets and other generalized closed sets are also examined.
This presentation provides an introduction to Galois fields, which are finite fields with a prime number of elements. The objectives are to discuss preliminaries like sets and groups, introduce Galois fields and provide examples, discuss related theorems, and describe the computational approach. A sample computation in FORTRAN verifies the theorem that any element in a Galois field can be expressed as the sum of two squares.
On Zα-Open Sets and Decompositions of ContinuityIJERA Editor
In this paper, we introduce and study the notion of Zα-open sets and some properties of this class of sets are investigated. Also, we introduce the class of A *L-sets via Zα-open sets. Further, by using these sets, a new decompositions of continuous functions are presented. (2000) AMS Subject Classifications: 54D10; 54C05; 54C08.
Abstract: In this paper, we define and study about a new type of generalized closed set called, g∗s-closed set.Its relationship with already defined generalized closed sets are also studied
Totally R*-Continuous and Totally R*-Irresolute Functionsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
(𝛕𝐢, 𝛕𝐣)− RGB Closed Sets in Bitopological SpacesIOSR Journals
In this paper we introduce and study the concept of a new class of closed sets called (𝜏𝑖, 𝜏𝑗)− regular generalized b- closed sets (briefly(𝜏𝑖, 𝜏𝑗)− rgb-closed) in bitopological spaces.Further we define and study new neighborhood namely (𝜏𝑖, 𝜏𝑗)− rgb- neighbourhood (briefly(𝜏𝑖, 𝜏𝑗)− rgb-nhd) and discuss some of their properties in bitopological spaces. Also, we give some characterizations and applications of it.
The document discusses using Plücker coordinates to determine if a set of homogeneous polynomials generate the vector space of higher degree polynomials when projected onto a quotient ring. It begins by defining Plücker coordinates and showing that for two quadratic generators, the cubic vector space has zero image if the Plücker quantity P1P3 - P22 is non-zero. It then aims to generalize this to three cubic generators and the quartic vector space.
The document discusses relations and functions. It defines relations as subsets of Cartesian products of sets and describes how to classify relations as reflexive, symmetric, transitive, or an equivalence relation. It also defines functions, including their domain, codomain, and range. It describes how to classify functions as injective, surjective, or bijective. Examples are provided to illustrate these concepts of relations and functions.
This document presents a mathematical theory on weak contractions in cone metric spaces. It begins by introducing concepts such as cone metric spaces, C-contractions, weak C-contractions, and f-contractions. It then defines a new concept of a C-f weak contraction, which generalizes previous weak contraction definitions. The main result proved is a coincidence point and common fixed point theorem for C-f weak contractions in complete cone metric spaces under certain conditions on the mappings. Examples and remarks are provided to show how the new C-f weak contraction definition generalizes previous contraction definitions.
In 2001 and 2003, Nakaok and Oda [3] and [4] introduced the notation of maximal open sets and minimal open sets in topological spaces. In 2010, Miguel, Saeid and Seithuti [2], introduced the notation of maximal θ-open sets and minimal θ -closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal α-open sets and minimal α -open sets and investigate some of their fundamental properties.
This document presents a method for finding the best polynomial approximation of degree one for a function over a given interval using the method of least parallelograms. It introduces the problem, outlines the main results which include theorems on the existence and properties of the least parallelogram and its relationship to the minimax polynomial. Examples are also provided to illustrate the method.
γ Regular-open sets and γ-extremally disconnected spacesAlexander Decker
This document introduces γ-regular-open sets in topological spaces with an operation γ. γ-Regular-open sets lie between γ-clopen and γ-open sets. The complement of a γ-regular-open set is γ-regular-closed. Several properties of γ-regular-open and γ-regular-closed sets are proved, including: the intersection of two γ-regular-open sets is γ-regular-open, and the union of two γ-regular-closed sets is γ-regular-closed. The concepts of γ-regular-open and regular open sets are shown to be independent, but coincide for γ-regular spaces.
The document provides an overview of the Chase Algorithm, which is used to determine if a dependency D follows from a given set of dependencies S. It begins with a recap of relevant concepts from first-order logic for database theory, including formulas, models/instances, semantics, and dependencies. It then introduces the Chase Algorithm, which rewrites D as much as possible using rules in S, checking if the result D' is a tautology. If so, D follows from S. The document also discusses embeddings of formulas into instances and the satisfiability and termination of the Chase.
Group Theory and Its Application: Beamer Presentation (PPT)SIRAJAHMAD36
This document provides an overview of a seminar presentation on group theory and its applications. The presentation covers topics such as the definition of groups, order of groups and group elements, modular arithmetic, subgroups, Lagrange's theorem, and Sylow's theorems. It also discusses some examples of groups and applications of group theory in fields like algebraic topology, number theory, and physics. The presentation aims to introduce fundamental concepts in modern algebra through group theory.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
δ ˆ – Closed Sets in Ideal Topological SpacesIOSR Journals
The document introduces the concept of δˆ-closed sets in ideal topological spaces. It defines a subset A to be δˆ-closed if the σ-closure of A is contained in every open set U containing A. Some basic properties of δˆ-closed sets are established, including that δ-closed, δ-I-closed, δg-closed, and δgˆ-closed sets are all δˆ-closed. However, the converse relationships are not always true. Examples are provided to illustrate the independence of these classes of closed sets.
11.[29 35]a unique common fixed point theorem under psi varphi contractive co...Alexander Decker
This document presents a unique common fixed point theorem for two self maps satisfying a generalized contraction condition in partial metric spaces using rational expressions. It begins by introducing basic definitions and lemmas related to partial metric spaces. It then presents the main theorem, which states that if two self maps T and f satisfy certain contractive and completeness conditions, including being weakly compatible, then they have a unique common fixed point. The proof considers two cases - when the sequences constructed from the maps are eventually equal, and when they are not eventually equal but form a Cauchy sequence. It is shown in both cases that the maps must have a unique common fixed point.
This document summarizes key concepts related to cluster points (also called limit or accumulation points) of a set in a topological space. It defines a cluster point as a point x such that every neighborhood of x contains at least one other point from the set. The derived set of a set A is the set of all cluster points of A. It is proven that the closure of A is equal to the union of A and its derived set. Additionally, if a point has a neighborhood containing only finitely many points from the set, it cannot be a cluster point, and if it is a cluster point every neighborhood must contain infinitely many points from the set.
This document summarizes key concepts related to cluster points (also called limit or accumulation points) of sets in topological spaces. It defines a cluster point as a point x such that every neighborhood of x contains at least one other point from the set. The closure of a set A is defined as the set of points that are either in A or are cluster points of A. Several theorems are presented, including: the closure of a set is the union of the set and its derived set (cluster points); a set is closed if it contains all its cluster points; and a finite set cannot have any cluster points.
This document introduces and studies the concept of ˆ-closed sets in topological spaces. Some key points:
1. ˆ-closed sets are defined as sets whose δ-closure is contained in any semi-open set containing the set.
2. It is shown that ˆ-closed sets lie between δ-closed sets and various other classes like δg-closed and ω-closed sets.
3. Several characterizations of ˆ-closed sets are provided in terms of properties of the difference between the δ-closure of the set and the set itself.
4. The concept of the ˆ-kernel of a set is introduced, defined as the intersection of all ˆ-
This document discusses generalized closed sets in topological spaces. It begins by introducing several types of generalized closed sets that have been defined in previous literature, such as g-closed sets, sg-closed sets, gs-closed sets, etc. It then defines a new type of generalized closed set called a g*s-closed set, which is a subset A such that the semi-closure of A is contained in every g-open set containing A. Examples are provided to illustrate g*s-closed sets. Properties of g*s-closed sets are discussed, such as every semi-closed set being g*s-closed, but the converse is not true. The relationship between g*s-closed sets and other
This document summarizes research on generalized β-closure spaces and β-connectedness. It defines key concepts such as β-closure functions, β-separated sets, and β-connectedness. Several important results are proven, including: (1) A set is β-connected if its subsets satisfy the Hausdorff-Lennes condition; (2) If a function between neighborhood spaces is β-continuous, the preimage of a β-connected set is β-connected; (3) The β-closure of a β-connected set is β-connected. The document establishes relationships between β-closure, β-separation, and β-connectedness in generalized closure spaces.
Some properties of gi closed sets in topological space.docxAlexander Decker
This document introduces generalized *i-closed (g*i-closed) sets in topological spaces and studies some of their properties. It defines what a g*i-closed set is and shows that every closed, i-closed, semi-closed, g-closed, gs-closed, and δg-closed set is also a g*i-closed set. However, the converses of these statements are not always true. Examples are provided to illustrate this. The relationships between g*i-closed sets and other generalized closed sets are also examined.
This presentation provides an introduction to Galois fields, which are finite fields with a prime number of elements. The objectives are to discuss preliminaries like sets and groups, introduce Galois fields and provide examples, discuss related theorems, and describe the computational approach. A sample computation in FORTRAN verifies the theorem that any element in a Galois field can be expressed as the sum of two squares.
On Zα-Open Sets and Decompositions of ContinuityIJERA Editor
In this paper, we introduce and study the notion of Zα-open sets and some properties of this class of sets are investigated. Also, we introduce the class of A *L-sets via Zα-open sets. Further, by using these sets, a new decompositions of continuous functions are presented. (2000) AMS Subject Classifications: 54D10; 54C05; 54C08.
Abstract: In this paper, we define and study about a new type of generalized closed set called, g∗s-closed set.Its relationship with already defined generalized closed sets are also studied
Totally R*-Continuous and Totally R*-Irresolute Functionsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
(𝛕𝐢, 𝛕𝐣)− RGB Closed Sets in Bitopological SpacesIOSR Journals
In this paper we introduce and study the concept of a new class of closed sets called (𝜏𝑖, 𝜏𝑗)− regular generalized b- closed sets (briefly(𝜏𝑖, 𝜏𝑗)− rgb-closed) in bitopological spaces.Further we define and study new neighborhood namely (𝜏𝑖, 𝜏𝑗)− rgb- neighbourhood (briefly(𝜏𝑖, 𝜏𝑗)− rgb-nhd) and discuss some of their properties in bitopological spaces. Also, we give some characterizations and applications of it.
The document discusses using Plücker coordinates to determine if a set of homogeneous polynomials generate the vector space of higher degree polynomials when projected onto a quotient ring. It begins by defining Plücker coordinates and showing that for two quadratic generators, the cubic vector space has zero image if the Plücker quantity P1P3 - P22 is non-zero. It then aims to generalize this to three cubic generators and the quartic vector space.
The document discusses relations and functions. It defines relations as subsets of Cartesian products of sets and describes how to classify relations as reflexive, symmetric, transitive, or an equivalence relation. It also defines functions, including their domain, codomain, and range. It describes how to classify functions as injective, surjective, or bijective. Examples are provided to illustrate these concepts of relations and functions.
This document presents a mathematical theory on weak contractions in cone metric spaces. It begins by introducing concepts such as cone metric spaces, C-contractions, weak C-contractions, and f-contractions. It then defines a new concept of a C-f weak contraction, which generalizes previous weak contraction definitions. The main result proved is a coincidence point and common fixed point theorem for C-f weak contractions in complete cone metric spaces under certain conditions on the mappings. Examples and remarks are provided to show how the new C-f weak contraction definition generalizes previous contraction definitions.
In 2001 and 2003, Nakaok and Oda [3] and [4] introduced the notation of maximal open sets and minimal open sets in topological spaces. In 2010, Miguel, Saeid and Seithuti [2], introduced the notation of maximal θ-open sets and minimal θ -closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal α-open sets and minimal α -open sets and investigate some of their fundamental properties.
This document presents a method for finding the best polynomial approximation of degree one for a function over a given interval using the method of least parallelograms. It introduces the problem, outlines the main results which include theorems on the existence and properties of the least parallelogram and its relationship to the minimax polynomial. Examples are also provided to illustrate the method.
γ Regular-open sets and γ-extremally disconnected spacesAlexander Decker
This document introduces γ-regular-open sets in topological spaces with an operation γ. γ-Regular-open sets lie between γ-clopen and γ-open sets. The complement of a γ-regular-open set is γ-regular-closed. Several properties of γ-regular-open and γ-regular-closed sets are proved, including: the intersection of two γ-regular-open sets is γ-regular-open, and the union of two γ-regular-closed sets is γ-regular-closed. The concepts of γ-regular-open and regular open sets are shown to be independent, but coincide for γ-regular spaces.
The document provides an overview of the Chase Algorithm, which is used to determine if a dependency D follows from a given set of dependencies S. It begins with a recap of relevant concepts from first-order logic for database theory, including formulas, models/instances, semantics, and dependencies. It then introduces the Chase Algorithm, which rewrites D as much as possible using rules in S, checking if the result D' is a tautology. If so, D follows from S. The document also discusses embeddings of formulas into instances and the satisfiability and termination of the Chase.
Group Theory and Its Application: Beamer Presentation (PPT)SIRAJAHMAD36
This document provides an overview of a seminar presentation on group theory and its applications. The presentation covers topics such as the definition of groups, order of groups and group elements, modular arithmetic, subgroups, Lagrange's theorem, and Sylow's theorems. It also discusses some examples of groups and applications of group theory in fields like algebraic topology, number theory, and physics. The presentation aims to introduce fundamental concepts in modern algebra through group theory.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
δ ˆ – Closed Sets in Ideal Topological SpacesIOSR Journals
The document introduces the concept of δˆ-closed sets in ideal topological spaces. It defines a subset A to be δˆ-closed if the σ-closure of A is contained in every open set U containing A. Some basic properties of δˆ-closed sets are established, including that δ-closed, δ-I-closed, δg-closed, and δgˆ-closed sets are all δˆ-closed. However, the converse relationships are not always true. Examples are provided to illustrate the independence of these classes of closed sets.
11.[29 35]a unique common fixed point theorem under psi varphi contractive co...Alexander Decker
This document presents a unique common fixed point theorem for two self maps satisfying a generalized contraction condition in partial metric spaces using rational expressions. It begins by introducing basic definitions and lemmas related to partial metric spaces. It then presents the main theorem, which states that if two self maps T and f satisfy certain contractive and completeness conditions, including being weakly compatible, then they have a unique common fixed point. The proof considers two cases - when the sequences constructed from the maps are eventually equal, and when they are not eventually equal but form a Cauchy sequence. It is shown in both cases that the maps must have a unique common fixed point.
This document summarizes key concepts related to cluster points (also called limit or accumulation points) of a set in a topological space. It defines a cluster point as a point x such that every neighborhood of x contains at least one other point from the set. The derived set of a set A is the set of all cluster points of A. It is proven that the closure of A is equal to the union of A and its derived set. Additionally, if a point has a neighborhood containing only finitely many points from the set, it cannot be a cluster point, and if it is a cluster point every neighborhood must contain infinitely many points from the set.
This document summarizes key concepts related to cluster points (also called limit or accumulation points) of sets in topological spaces. It defines a cluster point as a point x such that every neighborhood of x contains at least one other point from the set. The closure of a set A is defined as the set of points that are either in A or are cluster points of A. Several theorems are presented, including: the closure of a set is the union of the set and its derived set (cluster points); a set is closed if it contains all its cluster points; and a finite set cannot have any cluster points.
This document introduces and studies the concept of ˆ-closed sets in topological spaces. Some key points:
1. ˆ-closed sets are defined as sets whose δ-closure is contained in any semi-open set containing the set.
2. It is shown that ˆ-closed sets lie between δ-closed sets and various other classes like δg-closed and ω-closed sets.
3. Several characterizations of ˆ-closed sets are provided in terms of properties of the difference between the δ-closure of the set and the set itself.
4. The concept of the ˆ-kernel of a set is introduced, defined as the intersection of all ˆ-
This document discusses generalized closed sets in topological spaces. It begins by introducing several types of generalized closed sets that have been defined in previous literature, such as g-closed sets, sg-closed sets, gs-closed sets, etc. It then defines a new type of generalized closed set called a g*s-closed set, which is a subset A such that the semi-closure of A is contained in every g-open set containing A. Examples are provided to illustrate g*s-closed sets. Properties of g*s-closed sets are discussed, such as every semi-closed set being g*s-closed, but the converse is not true. The relationship between g*s-closed sets and other
On Fuzzy - Semi Open Sets and Fuzzy - Semi Closed Sets in Fuzzy Topologic...IOSR Journals
Abstract: The aim of this paper is to introduce the concept of fuzzy - semi open and fuzzy - semi closed sets of a fuzzy topological space. Some characterizations are discussed, examples are given and properties are established. Also, we define fuzzy - semi interior and fuzzy - semi closure operators. And we introduce fuzzy
- t-set, -SO extremely disconnected space analyse the relations between them.
MSC 2010: 54A40, 03E72.
This document provides an overview of preliminary topological concepts needed for applied mathematics. It defines topological spaces and metric spaces, and introduces key topological notions like open and closed sets, bases for topologies, convergence of sequences, accumulation points, interior and closure of sets, and dense sets. Metric spaces are shown to induce a natural topological structure, though not all topologies come from a metric. Examples are provided to illustrate various definitions and properties.
International Refereed Journal of Engineering and Science (IRJES) is a peer reviewed online journal for professionals and researchers in the field of computer science. The main aim is to resolve emerging and outstanding problems revealed by recent social and technological change. IJRES provides the platform for the researchers to present and evaluate their work from both theoretical and technical aspects and to share their views.
11. gamma sag semi ti spaces in topological spacesAlexander Decker
This document introduces the concept of γ-sαg*-semi Ti spaces where i = 0, 1/2, 1, 2. It defines γ-sαg*-semi open and closed sets. Properties of γ-sαg*-semi closure and γ-sαg*-semi generalized closed sets are discussed. It is shown that every γ-sαg*-semi generalized closed set is γ-semi generalized closed. A subset A is γ-sαg*-semi generalized closed if and only if the intersection of A with the γ-sαg*-semi closure of each point in the γ-closure of A is non-empty. The γ-sαg*-semi closure of a set
This document introduces the concept of γ-sαg*-semi Ti spaces where i = 0, 1/2, 1, 2. It defines γ-sαg*-semi open and closed sets. Properties of γ-sαg*-semi closure and γ-sαg*-semi generalized closed sets are discussed. It is shown that every γ-sαg*-semi generalized closed set is γ-semi generalized closed. The paper investigates when a space is a γ-sαg*-semi Ti space by looking at when γ-sαg*-semi generalized closed sets are γ-semi closed. It concludes that for each point x in a space, the singleton {x} is either γ-
This document introduces the concept of γ-sαg*-semi open sets in topological spaces and some of their properties. It begins by discussing previous related concepts like γ-open sets, γ-closure, and γ-semi open sets. It then defines what a γ-sαg*-semi open set is and establishes some basic properties. The main part of the document introduces and defines the concepts of γ-sαg*-semi Ti spaces for i=0, 1/2, 1, 2. It establishes properties of γ-sαg*-semi g-closed sets and proves several theorems about γ-sαg*-semi closure operators and their relationships to other concepts. The document contributes to the mathematical
The determination of this paper is to introduce two new spaces , namely 𝑆𝑔
∗
-compact and 𝑆𝑔
∗
-
connected spaces. Additionally some properties of these spaces are investigated.
Mathematics Subject Classification: 54A05
This document introduces and studies a new type of closed set called strongly τb-closed (τ*b-closed) sets. The following is summarized:
1. τ*b-closed sets are between closed sets and gsg-closed sets.
2. Properties and relationships of τ*b-closed sets are investigated, showing they are finer than τb-closed sets and contained within several other closed set classes.
3. Characterizations of τ*b-closed and τ*b-open sets are provided, such as the union of τ*b-closed sets being τ*b-closed.
This document introduces and investigates some weak separation axioms using the notion of πgb-closed sets. It defines πgb-closed sets, πgb-continuous functions, and various separation axioms including πgb-T0, πgb-T1, and πgb-T2. It introduces the concept of a πgb-D-set and defines associated properties like πgb-D0, πgb-D1, and πgb-D2 spaces. Results are proved relating these new concepts, showing properties like πgb-D1 spaces being πgb-T0 and πgb-D2 spaces being equivalent to
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Set and Set operations, UITM KPPIM DUNGUNbaberexha
This document defines sets and common set operations such as union, intersection, difference, complement, Cartesian product, and cardinality. It begins by defining a set as a collection of distinct objects and provides examples of sets. It then discusses ways to represent and visualize sets using listings, set-builder notation, Venn diagrams, and properties of subsets, supersets, equal sets, disjoint sets, and infinite sets. The document concludes by defining common set operations and identities using membership tables and examples.
Notions via β*-open sets in topological spacesIOSR Journals
In this paper, first we define β*-open sets and β*-interior in topological spaces.J.Antony Rex Rodrigo[3] has studied the topological properties of 𝜂 * -derived, 𝜂 * -border, 𝜂 * -frontier and 𝜂 * exterior of a set using the concept of 𝜂 * -open following M.Caldas,S.Jafari and T.Noiri[5]. By the same technique the concept of β*-derived, β*-border, β*-frontier and β*exterior of a set using the concept of β*-open sets are introduced.Some interesting results that shows the relationships between these concepts are brought about
On Extendable Sets in the Reals (R) With Application to the Lyapunov Stabilit...BRNSS Publication Hub
This document summarizes a research article that defines extendable sets in the real numbers (R) and applies this concept to the Lyapunov stability comparison principle of ordinary differential equations. It begins with the author's own definition of extension on R and a basic result called the basic extension fact for R. It then reviews existing definitions and theorems on extension, including Urysohn's lemma and Tietze's extension theorem. The document concludes by extensively applying these results to prove some important results relating to the comparison principle of Lyapunov stability theory in ordinary differential equations.
Contra * Continuous Functions in Topological SpacesIJMER
This document discusses contra α* continuous functions between topological spaces. It begins by introducing α*-open sets and various related concepts like α*-continuity. It then defines a function from one topological space to another to be contra α*-continuous if the preimage of every open set is α*-closed in the domain space. Some properties of contra α*-continuous functions are established, including that every contra-continuous function is contra α*-continuous. Examples are given to show the concepts are independent. The discussion considers the relationships between contra α*-continuity and other variations of contra-continuity.
This document presents a study that uses linear regression to predict university freshmen's academic performance (GPA) based on their scores on the Joint Matriculation Examination (JME). The study finds a weak positive correlation (R=0.137) between GPA and JME scores, with the regression model only explaining 1.9% of variability in GPA. Statistical tests show no significant relationship between JME score and university GPA (p>0.05). The study concludes that JME score is not a strong predictor of freshmen academic performance.
This document describes a school bus tracking and security system that uses face recognition, GPS, and notification technologies. The system uses a camera to identify students as they board and exit the bus. A GPS module tracks the bus location and uploads coordinates to a database. Parents and school administrators can access this information through a mobile app to track students. When a student's face is recognized, a notification is sent to the parents. The system aims to increase student safety by monitoring their locations and notifying parents when they enter or exit the bus.
BigBasket encashing the Demonetisation: A big opportunityIJSRED
1. BigBasket is India's largest online grocery retailer, launched in 2011 when online grocery shopping was still nascent.
2. During India's 2016 demonetization, when cash was scarce, online grocery saw a major boost as consumers turned to sites like BigBasket for contactless digital payments.
3. However, BigBasket faced challenges in meeting consumer expectations for quick delivery while expanding partnerships with local vendors for fresh produce during this surge in demand.
Quantitative and Qualitative Analysis of Plant Leaf DiseaseIJSRED
This document discusses a technique for detecting plant leaf diseases using image processing. It begins with an introduction to plant pathology and the importance of identifying plant diseases. Common plant leaf diseases like Alternaria Alternata, Anthracnose, Bacterial blight, and Cercospora Leaf Spot are described along with their symptoms. The existing methods of disease identification are discussed. The proposed method uses various image processing techniques like filtering, histogram equalization, k-means clustering, and Gray Level Co-occurrence Matrix (GLCM) feature extraction to detect diseases. Image quality is then assessed to identify the affected regions of the leaf.
DC Fast Charger and Battery Management System for Electric VehiclesIJSRED
This document discusses the development of a DC fast charger and battery management system for electric vehicles. It aims to reduce charging times for EVs by designing an efficient charging mechanism. A PIC microcontroller controls the charging voltage and a battery management system monitors battery temperature, voltage, current and provides notifications. The system uses a step-down transformer, rectifier, voltage regulators and temperature sensor to charge lithium-ion batteries safely and quickly, while the battery management system protects the batteries from overcharging or overheating. Faster charging times through more charging stations could encourage greater adoption of electric vehicles.
France has experienced steady economic growth through policies that develop human capital and innovation. It has a highly organized education system that has increased enrollments over time, particularly in tertiary education. France also invests heavily in research and development, ranking highly in patents and innovative organizations. Infrastructure investment has also increased tangible capital stock. Additionally, factors like political stability, rule of law, and low corruption create an environment conducive to business investment and growth. Major events like the French Revolution helped shape France culturally, legally and technologically in ways that still influence its growth path today.
This document describes an acquisition system designed to make the examination process more efficient. The system uses a Raspberry Pi to control various hardware components including an RFID reader, rack and pinion assembly, and motor. It is intended to reduce the time and effort required of staff to distribute exam materials by automating the process. When examiners scan their RFID tags, the system verifies their identity and allows them to retrieve the appropriate exam bundles via a motorized rack and pinion assembly. The goal is to minimize manual labor and speed up exam distribution using an automated hardware and software solution controlled by a Raspberry Pi microcontroller.
Parallelization of Graceful Labeling Using Open MPIJSRED
This document summarizes research on parallelizing the graceful graph labeling problem using OpenMP on multi-core processors. It introduces the concepts of parallelization, multi-core architecture, and OpenMP. An algorithm is designed to parallelize graceful labeling by distributing graph vertices across processor cores. Execution time and speedup are measured for graphs of increasing size, showing improved speedup and reduced time with parallelization. Results show consistent performance gains as graph size increases due to better utilization of the multi-core architecture.
Study of Phenotypic Plasticity of Fruits of Luffa Acutangula Var. AmaraIJSRED
This study examines the phenotypic plasticity of fruits in the plant Luffa acutangula var. amara across different locations in Sindhudurg district, Maharashtra, India. The study found that the plant exhibited plasticity in growth cycle, flowering season, leaf shape, and fruit size depending on location. Maximum fruit weights and sizes were recorded at Talebazar village, while minimum sizes were found at Dahibav village. The variation in fruit morphology is an adaptation to the different environmental conditions at each site.
Understanding Architecture of Internet of ThingsIJSRED
The document discusses the architecture of the Internet of Things (IoT). It begins by introducing IoT and its key components. It then discusses three traditional IoT architectures: (1) a three-layer architecture consisting of a perception, network and application layer; (2) the TCP/IP four-layer model; and (3) the Telecommunications Management Network's five-layer logical layered architecture. The document proposes a new five-layer IoT architecture combining aspects of these models. The five layers are the business, application, processing, transport and perception layers. The perception layer collects data via sensors while the business layer manages the overall enterprise.
This document describes a project report submitted by three students for their bachelor's degree. The report outlines the development of a smart shopping cart system that utilizes RFID and Zigbee technologies. The smart cart is intended to enhance the shopping experience for customers by automatically billing items as they are added to the cart, providing real-time stock levels, and reducing checkout times. The system aims to benefit both customers through a more personalized shopping experience and retailers by improving stock management and reducing shoplifting. The document includes sections on requirements, system design, implementation, results and discussion, and conclusions.
An Emperical Study of Learning How Soft Skills is Essential for Management St...IJSRED
This document discusses an empirical study on the importance of soft skills for management students' careers. It finds that while hard skills and academic performance were once prioritized by employers, soft skills like communication, teamwork, and emotional intelligence are now essential for success. The study surveyed 50 management students and faculty in Bangalore to understand how well soft skills training is incorporated and its benefits. It determined that soft skills like communication are crucial as they influence interactions and job performance. However, older teaching methods do not sufficiently develop these skills. Integrating soft skills training into courses could better prepare students for today's work challenges.
The document describes a proposed smart canteen management system that uses various technologies like a web application, barcode scanner, and thermal printer to automate the food ordering process. The system aims to reduce wait times for students and avoid food wastage by allowing online ordering and monitoring stock. A barcode scanner will be used to identify students during ordering and payment. Thermal printers will generate receipts. The system is expected to reduce workload for staff and provide detailed sales reports for management.
This document discusses Gandhi's concept of trusteeship as an alternative economic system. It summarizes that Gandhi did not distinguish between economics and ethics, and based trusteeship on religious ideas like non-possession and truth as well as Western ideas like stewardship. Trusteeship aimed to persuade wealthy property owners to hold wealth in trust for the benefit of society rather than personal gain. It was meant as a non-violent alternative to capitalism and communism that eliminated class conflict through cooperation and trust between rich and poor. The document provides background on the philosophical and religious influences on Gandhi's views before explaining the key aspects of his theory of trusteeship.
Impacts of a New Spatial Variable on a Black Hole Metric SolutionIJSRED
This document discusses the impacts of introducing a new spatial variable in black hole metrics. It begins by summarizing Einstein and Rosen's 1935 paper which introduced a variable ρ = r - 2M in the Schwarzschild metric to remove the singularity. The document then introduces a similar new variable p = r - 2√M and analyzes how this impacts the Schwarzschild metric. Specifically, it notes that this new variable allows for negative radii values and multiple asymptotic regions beyond just two, introducing concepts of probability and imaginary spatial coordinates. Overall, the document explores how different mathematical variables can impact theoretical physics concepts like wormholes.
A Study to Assess the Effectiveness of Planned Teaching Programme on Knowledg...IJSRED
This document summarizes a study that assessed the effectiveness of a planned teaching program on mothers' knowledge of preventing acute respiratory infections in children under 5. 50 mothers were surveyed before and after the program. Before, 36% had moderate knowledge, 62% had inadequate knowledge, and 2% had adequate knowledge. After, 34% had moderate knowledge, 0% had inadequate knowledge, and 66% had adequate knowledge, showing the program improved mothers' knowledge. The study found no significant association between mothers' knowledge and factors like age, education, or family type.
This document describes a proposed ingenuous Trafalgar contrivition system to improve traffic flow and emergency vehicle access. The system uses embedded technologies like a Raspberry Pi, RF transmitter and receiver, and an Android app. When an emergency vehicle is detected approaching a traffic light, the system will open the lights on its path without disrupting other signals. The app will also help identify hit-and-run vehicles through a brief tracking period. The goal is to reduce traffic congestion and response times to save lives.
This document discusses a proposed system called the Farmer's Analytical Assistant, which aims to help farmers in India maximize crop yields through predictive analysis and recommendations. It analyzes agricultural data on factors like soil properties, rainfall, and past crop performance using machine learning techniques to predict optimal crops for different regions based on the environmental conditions. The proposed system would allow farmers to input local data, receive personalized yield predictions and crop suggestions, and get advice from experts online. The methodology section describes how climate/rainfall and soil data is collected and analyzed using machine learning models to provide crop recommendations. The goal is to improve upon traditional crop selection methods and help increase farmers' incomes.
Functions of Forensic Engineering Investigator in IndiaIJSRED
Forensic engineering involves applying engineering principles and methodologies to answer legal questions, especially regarding accidents and failures. A forensic engineer investigates failures through failure analysis and root cause analysis to determine how and why something failed. The engineer must be familiar with relevant codes and standards, understand eyewitness testimony, apply the scientific method to reconstruct events, and report findings clearly to assist courts. A forensic engineering investigation follows the scientific method to methodically analyze evidence and test hypotheses to determine the cause and circumstances of a failure or accident.
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSIJNSA Journal
The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapte...University of Maribor
Slides from talk presenting:
Aleš Zamuda: Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapter and Networking.
Presentation at IcETRAN 2024 session:
"Inter-Society Networking Panel GRSS/MTT-S/CIS
Panel Session: Promoting Connection and Cooperation"
IEEE Slovenia GRSS
IEEE Serbia and Montenegro MTT-S
IEEE Slovenia CIS
11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.