Excluded Point Topology is T4/Proof 2

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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.

$\blacksquare$