Arens-Fort Space is Separable

Theorem

Let $T = \struct {S, \tau}$ 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

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $26$. Arens-Fort Space: $4$