Dispersion Point of Excluded Point Space

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

Then $p$ is a dispersion point of $T$.

Proof
We have that the Excluded Point Topology is Open Extension Topology of Discrete Topology.

So $S \setminus \left\{{p}\right\}$ is a discrete space.

Then a discrete space is totally disconnected.

The result follows from definition of dispersion point.