Finite Space is Sequentially Compact

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

Then $T$ is sequentially compact.

Proof

 * Finite Topological Space is Compact.
 * Compact Space is Countably Compact.
 * Finite Space is Second-Countable.
 * Second-Countable Space is First-Countable.
 * First-Countable Space is Sequentially Compact iff Countably Compact.

Hence the result.