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Extensions of functions which preserve the continuity on the original domain. (English) Zbl 0986.54025
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).
Reviewer: K.P.Hart (Delft)

MSC:
54C20 Extension of maps
54E50 Complete metric spaces
03E15 Descriptive set theory
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