Arens-Fort Space is Separable

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Theorem

Let $T = \left({S, \tau}\right)$ be the Arens-Fort space.


Then $T$ is a separable space.


Proof

We have that the Arens-Fort space is an expansion of a countable Fort space.

So $S$ is countable.

The result follows from Countable Space is Separable.

$\blacksquare$


Sources