Category:Definitions/T3 Spaces

This category contains definitions related to $T_3$ spaces in the context of topology.
Related results can be found in Category:T3 Spaces.

$T = \struct {S, \tau}$ is a $T_3$ space if and only if:

$\forall F \subseteq S: \relcomp S F \in \tau, y \in \relcomp S F: \exists U, V \in \tau: F \subseteq U, y \in V: U \cap V = \O$

That is, for any closed set $F \subseteq S$ and any point $y \in S$ such that $y \notin F$ there exist disjoint open sets $U, V \in \tau$ such that $F \subseteq U$, $y \in V$.