Excluded Point Topology is T4/Proof 2

Theorem

Let $T = \struct {S, \tau_{\bar p} }$ 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.

$\blacksquare$