# Compact Space in Particular Point Space

## Theorem

Let $T = \struct {S, \tau_p}$ be a particular point space.

Then $\set p$ is compact in $T$.

## Proof

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

So $\set p$ is compact in $T$.

$\blacksquare$