Arens-Fort Space is Lindelöf

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Theorem

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


Then $T$ is a Lindelöf space.


Proof

We have:

The Arens-Fort Space is Sigma-Compact.
A $\sigma$-compact space is Lindelöf.

$\blacksquare$


Sources