# Ultraconnected Space is Connected

## Theorem

Let $T = \left({S, \tau}\right)$ be a topological space which is ultraconnected.

Then $T$ is connected.

## Proof

Let $T = \left({S, \tau}\right)$ 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.

$\blacksquare$