Ultraconnected Space is Connected

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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.

$\blacksquare$


Sources