Arens-Fort Space is not Compact

Theorem

Let $T = \struct {S, \tau}$ be the Arens-Fort space.

Then $T$ is not a compact space.

Proof

We have:

The Arens-Fort Space is not Weakly Locally Compact.

A Compact Space is Weakly Locally 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: $4$