$T4$ space

Definition 1.

[1] Suppose $X$ is a topological space. Further, suppose that for any two disjoint closed sets $A\mathrm{,}B\mathrm{\subseteq }X$, there are two disjoint open sets $U$ and $V$ such that $A\mathrm{\subseteq }U$ and $B\mathrm{\subseteq }V$. Then we say that $X$ is a $T_{\mathrm{4}}$ space.

Notes

It should be pointed out that there is no standard convention for separation axioms in topology. The above definition follows [1]. However, in some references (e.g. [2]) the meaning of $T_4$ and normal are exchanged.

Title	$T4$ space
Canonical name	T4Space
Date of creation	2013-03-22 14:42:15
Last modified on	2013-03-22 14:42:15
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	5
Author	matte (1858)
Entry type	Definition
Classification	msc 54D15
Related topic	SeparationAxioms
Related topic	HowIsNormalityAndT4DefinedInBooks