Extensions of functions which preserve the continuity on the original domain (Q1567309)

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).