Arens-Fort Space is Sigma-Compact/Proof 2

Theorem

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

Then $T$ is a $\sigma$-compact space.

Proof

The result follows from Arens-Fort Space is Countable and Countable Space is Sigma-Compact.

$\blacksquare$

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: $4$