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

$\blacksquare$

Also see

• Irreducible Space is not necessarily Path-Connected