Double Pointed Fortissimo Space is not Sigma-Compact

Theorem

Let $T = \struct {S, \tau}$ be a Fortissimo space.

Let $T \times D$ be the double pointed topology on $T$.

Then $T \times D$ is not $\sigma$-compact.

Proof

This theorem requires a proof. In particular: Use the same argument as Fortissimo Space is not Sigma-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: $25$. Fortissimo Space: $4$