Let (X,T) be a topological space,.A subset X. Suppose that for all x .pdf

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Let (X,T) be a topological space,.A subset X. Suppose that for all x epsilon A, U epsilon T s.t. x epsilon U subset A. Show that.4 is open in X. Solution take the union of all such open sets i.e. Union of U_x for all x in A Union U_x is open since U_x is open for all x. and Union U_x = A (Union U_x is a subset of A and A is subset of Union U_x) So A is open.

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Lists can contain other lists as elements. For example the list HAIRY=[1,2,[3,4,[5,[6,7.8],[9,10]],11,[12,[13,14],[15,16]]]] contains several lists containing other lists -- ie it is a \"multilevel\" list. Write a function flatten(L) which takes a possibly multilevel list L as an argument and returns a new list with the same elements in the same overall order as L but with only one level. For example, flatten(HAIRY) would return the list [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] Solution Please find the required program along with its output. Please see the comments against each line to understand the step. def flatten(L): #recursive function to flatten a list for element in L: #iterate through each element of a list if not isinstance(element, list): # if the element is not a list, yield element # just return the element else: #if the element is a list, then recursivley call the flatten fucntion on the sub list, and return each element individually for x in flatten(element): yield x print \"Flattened list elements are: \" for x in flatten([1,2,[3,4,[5,[6,7,8],[9,10]],11,[12,[13,14],[15,16]]]]): print x, #print the flatten list elements ---------------------------------------- OUTPUT : Flattened list elements are: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16.

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Match the modified stem to its correct definition. Stolon Rhizome Tuber Bulb Corm Stem succulence Cladophyll A simple modified stem that stores starch below ground, like a potato. A belowground modified stem consisting of many compressed internodes with whorls of leaves surrounding and protecting the stem. Stems that have become modified to store water and serve as a primary photosynthetic organ in desert environments. A stem that has been modified to resemble a leaf. A modified stem that grows horizontally below the surface of the ground. A modified stem that grows horizontally above the surface of the ground. A belowground modified stem for storing starch consisting of a single thick internode wrapped in papery leaves. - A. B. C. D. E. F. G. Stolon - A. B. C. D. E. F. G. Rhizome - A. B. C. D. E. F. G. Tuber - A. B. C. D. E. F. G. Bulb - A. B. C. D. E. F. G. Corm - A. B. C. D. E. F. G. Stem succulence - A. B. C. D. E. F. G. CladophyllA. A simple modified stem that stores starch below ground, like a potato.B. A belowground modified stem consisting of many compressed internodes with whorls of leaves surrounding and protecting the stem.C. Stems that have become modified to store water and serve as a primary photosynthetic organ in desert environments.D. A stem that has been modified to resemble a leaf.E. A modified stem that grows horizontally below the surface of the ground.F. A modified stem that grows horizontally above the surface of the ground.G. A belowground modified stem for storing starch consisting of a single thick internode wrapped in papery leaves. Solution Stem succulence - a modified stem to store water and serve as a primary photosynthesis organ in desert environment and condition..!! Cladophyll - I is the stem which is being modified to resemble as a leaf which can perform photosynthesis too..!! Eg:- Asparagus. Bulb- a below ground modified stem consisting of many compressed internode with whorls of leaves surrounding and protecting the main interior middle stem.. Eg:- onion..!! Tuber- a simple modified stem that stores starch below ground, like a potato..!! Corm- a below ground modified stem for storing starch consisting of a single thick internode wrapped in papery leaves..!! Rhizome - a modified stem that grows horizontally below the surface of the ground which can form adventitious roots and shoots.. Stolon - a modified stem that grows horizontal above the surface of the ground.. They are called runner...

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