Fort Space is Compact

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

Then $T$ is a compact space.

Proof
Let $\mathcal C$ be an open cover of $T$.

Then $\exists U \in \mathcal C$ such that $p \in U$ and so $\complement_S \left({U}\right)$ is finite.

For each $x \in \complement_S \left({U}\right)$ there exists some $C_x \in \mathcal C$ such that $x \in C$.

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

Hence the result by definition of compact space.