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.

Title	completely normal
Canonical name	CompletelyNormal
Date of creation	2013-03-22 12:13:51
Last modified on	2013-03-22 12:13:51
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	7
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 54-00
Synonym	complete normality
Related topic	NormalTopologicalSpace