Category:Definitions/Completely Hausdorff Spaces

This category contains definitions related to Completely Hausdorff Spaces in the context of topology.
Related results can be found in Category:Completely Hausdorff Spaces.

$\struct {S, \tau}$ is a completely Hausdorff space or $T_{2 \frac 1 2}$ space if and only if:

$\forall x, y \in S, x \ne y: \exists U, V \in \tau: x \in U, y \in V: U^- \cap V^- = \O$

That is, for any two distinct elements $x, y \in S$ there exist open sets $U, V \in \tau$ containing $x$ and $y$ respectively whose closures are disjoint.