# Category:Completely Hausdorff Spaces

This category contains results about Completely Hausdorff Spaces in the context of Topology.

$\left({S, \tau}\right)$ is a **completely Hausdorff space** or **$T_{2 \frac 1 2}$ space** if and only if:

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

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.

That is:

- $\left({S, \tau}\right)$ is a
**$T_{2 \frac 1 2}$ space**if and only if every two points in $S$ are separated by closed neighborhoods.

## Pages in category "Completely Hausdorff Spaces"

The following 14 pages are in this category, out of 14 total.