Discrete Space is Strongly Locally Compact

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space where $\tau$ is the discrete topology on $S$.

Then $T$ is strongly locally compact.

Proof
From Point in Discrete Space is Neighborhood, every point $x \in S$ is contained in an open set $\left\{{x}\right\}$.

Then from Interior Equals Closure of Subset of Discrete Space we have that $\left\{{x}\right\}$ equals its closure.

From Singleton Sets in Discrete Space are Compact, we have that $\left\{{x}\right\}$ is compact.

Hence the result by definition of strongly locally compact.