completely normal

Let $X$ be a topological space. $X$ is said to be if whenever $A,B\subseteq X$ with $A\cap \overline{B}=\overline{A}\cap B=\mathrm{\varnothing }$, then there are disjoint open sets $U$ and $V$ such that $A\subseteq U$ and $B\subseteq V$.

Equivalently, a topological space $X$ is if and only if every subspace is normal.