Extensions of functions which preserve the continuity on the original domain (Q1567309)
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scientific article; zbMATH DE number 1455639
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extensions of functions which preserve the continuity on the original domain |
scientific article; zbMATH DE number 1455639 |
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Extensions of functions which preserve the continuity on the original domain (English)
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6 June 2002
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The authors consider pairs \((X,Y)\) of spaces to be `good' if for every \(A\subseteq X\) every continuous \(f:A\to Y\) has an extension \(\overline f:X\to Y\) that is continuous at every point of~\(A\). Results include: every pair \((X,Y)\) with \(X\) metrizable and \(Y\) locally compact is good; \(X\)~is hereditarily (collectionwise) normal iff \((X,\mathbb R)\) is good (\((X,\kappa)\)~is good, where \(\kappa=w(X)\) carries the discrete topology).
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continuous map
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extensions of maps
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points of continuity
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