Ultraconnected Space is Connected

Theorem
Let $T = \struct {S, \tau}$ be a topological space which is ultraconnected.

Then $T$ is connected.

Proof
Let $T = \struct {S, \tau}$ be a topological space which is ultraconnected.

From Ultraconnected Space is Path-Connected, $T$ is path-connected.

The result follows from Path-Connected Space is Connected.