# completely normal

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

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

Title completely normal CompletelyNormal 2013-03-22 12:13:51 2013-03-22 12:13:51 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Definition msc 54-00 complete normality NormalTopologicalSpace