Countable Fort Space is Metrizable

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Theorem

Let $T = \struct {S, \tau_p}$ be a Fort space on a countably infinite set $S$.


Then $T$ is a metrizable space.


Proof

We have:

Fort Space is Regular
Countable Fort Space is Second-Countable.

The result follows from Urysohn's Metrization Theorem.

$\blacksquare$


Sources