# Ordinal Space is Strongly Locally Compact

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## Theorem

Let $T$ denote an ordinal space on a limit ordinal $\Gamma$.

Then $T$ is a strongly locally compact space.

## Proof

This theorem requires a proof.Demonstrated by showing that the closure of each basis neighborhood is compact.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*(2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $40 \text { - } 43$. Ordinal Space: $6$