Arens-Fort Space is Separable
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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: $4$