# Neighborhood of Origin in Arens-Fort Space is not Compact

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## Theorem

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

Let $N_p$ be a neighborhood of the point $p = \left({0, 0}\right)$.

Then $N_p$ is not compact.

## Proof

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{II}: \ 26: \ 4$