Infinite Particular Point Space is not Strongly Locally Compact

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

Then $T$ is not strongly locally compact.

Proof
Let $x \in S: x \ne p$.

Let $x \in U$ where $U$ is open in $T$.

From Closure of Open Set of Particular Point Space we have:
 * $U^- = S$

where $U^-$ is the closure of $U$.

But from Infinite Particular Point Space is Not Compact we have that $S$ is not compact.

Hence the result, by definition of strongly locally compact.