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About extensions of mappings into 
topologically complete spaces 
Radu Dumbraveanu 
Alecu Russo Balti State University 
IM...
Terminology 
Every space is considered to be a completely regular T1-space. 
A regular space X is said to be zero-dimensio...
nite open cover of X can be re
ned to a 
partition of X into clopen sets. 
R. Dumbraveanu Extensions of mappings into topologically complete spaces
Terminology 
It is well known that: 
for any metric space X, IndX = dimX; 
if X is Lindelof then indX = 0 if and only if ...
Terminology 
A topological space X is Dieudonne complete if there exists a 
complete uniformity on the space X. 
A space X...
About extensions of mappings into topologically complete spaces
About extensions of mappings into topologically complete spaces
About extensions of mappings into topologically complete spaces
About extensions of mappings into topologically complete spaces
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About extensions of mappings into topologically complete spaces

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About extensions of mappings into topologically complete spaces

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About extensions of mappings into topologically complete spaces

  1. 1. About extensions of mappings into topologically complete spaces Radu Dumbraveanu Alecu Russo Balti State University IMCS-50 August 19-23, 2014 Chisinau, Republic of Moldova R. Dumbraveanu Extensions of mappings into topologically complete spaces
  2. 2. Terminology Every space is considered to be a completely regular T1-space. A regular space X is said to be zero-dimensional if it is of small inductive dimension zero (indX = 0), i.e. X has a base of clopen sets. A normal space X has large inductive dimension zero (IndX = 0) if and only if for any two disjoint closed subsets A and B of X there is a clopen set C such that A C and B (X n C). A normal space X has Lebesgue covering dimension zero (dimX = 0) if any
  3. 3. nite open cover of X can be re
  4. 4. ned to a partition of X into clopen sets. R. Dumbraveanu Extensions of mappings into topologically complete spaces
  5. 5. Terminology It is well known that: for any metric space X, IndX = dimX; if X is Lindelof then indX = 0 if and only if IndX = 0; if X is normal then IndX = 0 if and only if dimX = 0. R. Dumbraveanu Extensions of mappings into topologically complete spaces
  6. 6. Terminology A topological space X is Dieudonne complete if there exists a complete uniformity on the space X. A space X is topologically complete if X is homeomorphic to a closed subspace of a product of metrizable spaces. The Dieudonne completion X of a space X is a topological complete space for which X is a dense subspace of X and each continuous mapping g from X into a topologically complete space Y admits a continuous extension g over X. A family fF : 2 Ag of the space X is functionally discrete if there exists a family ff : 2 Ag of continuous functions on X such that the family ff

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