Countable Complement Space is Locally Connected

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Theorem

Let $T = \struct {S, \tau}$ be a countable complement topology on an uncountable set $S$.


Then $T$ is a locally connected space.


Proof

We have that a Countable Complement Space is Irreducible.

The result follows from Irreducible Space is Locally Connected.

$\blacksquare$


Sources