Neighborhood of Origin in Arens-Fort Space is not Compact

Theorem

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

Let $N_p$ be a neighborhood of the point $p = \tuple {0, 0}$.

Then $N_p$ is not compact.

Proof

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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: $4$