Particular Point Topology is Closed Extension Topology of Discrete Topology

Theorem
Let $S$ be a set and let $p \in S$.

Let $\tau_p$ be the particular point topology on $S$.

Let $T = \left({S \setminus \left\{{p}\right\}, \vartheta}\right)$ be the discrete topological space on $S \setminus \left\{{p}\right\}$.

Then $T^* = \left({S, \tau_p}\right)$ is a closed extension space of $T$.

Proof
Directly apparent from the definitions of particular point topology, discrete topological space and closed extension space.