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

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