Excluded Point Topology is T4/Proof 2

Theorem

Let $T = \left({S, \tau_{\bar p}}\right)$ be an excluded point space.

Then $T$ is a $T_4$ space.

Proof

We have:

Excluded Point Topology is Open Extension Topology of Discrete Topology
Open Extension Topology is $T_4$

Hence the result.

$\blacksquare$