Dispersion Point in Particular Point Space

Theorem
Let $T = \left({S, \vartheta_p}\right)$ be a particular point space.

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

Proof
The space $S \setminus \left\{{p}\right\}$ is discrete.

From Totally Disconnected and Locally Connected Space is Discrete we have that $S \setminus \left\{{p}\right\}$ is totally disconnected.

Hence the result, from definition of dispersion point.