Excluded Point Space is Compact

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

Then $T$ is a compact space.

Proof
We have:
 * Excluded Point Topology is Open Extension Topology of Discrete Topology
 * Open Extension Space is Compact

Alternatively, the same argument can be used as for Open Extension Space is Compact.