Countable Space is Sigma-Compact

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space, where $S$ is a countable set.

Then $T$ is $\sigma$-compact.

Proof
From Finite Space Satisfies All Compactness Properties, for every $p \in S$, $\left\{{p}\right\}$ is compact.

Then $\displaystyle S = \bigcup_{p \mathop \in S} \left\{{p}\right\}$ is a countable union of compact sets.

Thus by definition $T$ is $\sigma$-compact.