Perfectly normal space
= Perfectly normal space
A <T1 space> is perfectly normal when it is normal and every closed subset is a <G-delta set>. Equivalently every closed subset is the <zero set of a continuous function> into $[0,1]$, using the <closed G-delta set as a zero set> theorem. If disjoint closed sets are the exact zero sets of $f,g$, then $f/(f+g)$ has those sets as its exact zero and one levels. Every subspace is normal, although the converse fails.