Irreducible Space with Finitely Many Open Sets is Path-Connected

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

Let its topology $\tau$ be finite.

Then $T$ is path-connected.

Proof
Follows immediately from:
 * Irreducible Space with Finitely Many Open Sets has Generic Point
 * Topological Space with Generic Point is Path-Connected

Also see

 * Irreducible Space is not necessarily Path-Connected