Fort Space is Compact

Theorem
Let $T = \struct {S, \tau_p}$ be a Fort space on an infinite set $S$.

Then $T$ is a compact space.

Proof
Let $\CC$ be an open cover of $T$.

Then $\exists U \in \CC$ such that $p \in U$ and so $\relcomp S U$ is finite.

For each $x \in \relcomp S U$ there exists some $C_x \in \CC$ such that $x \in C$.

So $U$, together with each of those $C_x \in \CC$, is a finite subcover of $\CC$.

Hence the result by definition of compact space.