Ordinal Space is Strongly Locally Compact

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. In particular: 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: $6$