Discrete Space is Compact iff Finite

Theorem
Let $T = \left({S, \vartheta}\right)$ be a topological space where $\vartheta$ is the discrete topology on $S$.

Let $S$ be an finite set, thereby making $\vartheta$ the finite discrete topology on $S$.

Then $T$ is compact.

Proof
A direct application of Finite Topological Space is Compact.