Compact Space in Particular Point Space

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

Then $\left\{{p}\right\}$ is compact in $T$.

Proof
Any open cover of $\left\{{p}\right\}$ has a finite subcover: any single set that contains $p$ is a cover for $\left\{{p}\right\}$.

So $\left\{{p}\right\}$ is compact in $T$.

Also see

 * Finite Topological Space is Compact