Finite Space is Sequentially Compact

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

Then $T$ is sequentially compact.

Proof
We have:


 * 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.