C-embedded subset
= C-embedded subset
{c}
{title2=$C(Y)=C(X)|_Y$}
A <subset> $Y\subseteq X$ is <C-embedded subset>[C-embedded] if every <continuous> <real-valued function> on its <subspace topology> extends continuously to $X$. <Closed subsets> of <normal spaces> have this property by the <Tietze extension theorem>. The condition also makes sense for nonclosed <subsets>.