Geoffrey Sangston

Theorem Suggestion: Locally compact + Has a group topology => Paracompact

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## Theorem Suggestion If a space is: - [Locally compact P130](https://topology.pi-base.org/properties/P000130) - [Has a group topology P87](https://topology.pi-base.org/properties/P000087) then it is [Paracompact P30](https://topology.pi-base.org/properties/P000030) ## Rationale This theorem would demonstrate that no...

Property Suggestion: locally contractible

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## Property Suggestion Primed versions are supposed to be equivalent. 1. (locally contractible in the sense of Borsuk.) For every $x \in X$, each neighborhood $U$ of $x$ contains a...

Space Suggestion: Connected compact locally 1-Euclidean spaces with cut points

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## Space Suggestion I was working on adding the circle with two origins and I noticed a space matching the title is missing: [π-Base, Search for `compact + Locally $n$-Euclidean...

## Space Suggestion Let $X = S^1 \sqcup \\{p\\}$. A nonempty set is open if and only if it equals $X$ or is an open subset of $S^1$. This is...

## Space Suggestion Let $X$ be $S^3$ = Three-dimensional sphere = Unit quaternions. Defined as in [Sphere](https://topology.pi-base.org/spaces/S000169). - For a reference to the unit quaternions / group structure of $S^3$,...

Trait Suggestion: Novak space S109 is extremally disconnected

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## Trait Suggestion The space Novak space [S109](https://topology.pi-base.org/spaces/S000109) is extremally disconnected P49, but this fact is not known to pi-Base today: [link to pi-Base](https://topology.pi-base.org/spaces/S000109/properties/P000049). (This issue began with the suggestion...

Property suggestion: 'Has a cofinite topology'

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I was wondering what the community thinks about the following property? - 'Has a cofinite topology' (S15 + S16, and the finite discrete spaces) I think many of the traits...

Trait Suggestion: 'Countable sigma-product of succesor to first uncountable ordinal' S181 is not Connected P36

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## Trait Suggestion [S000181](https://topology.pi-base.org/spaces/S000181) is not connected. ## Proof/References The projection $(\omega_1 + 1)^\omega \to \omega_1 + 1$ onto the first coordinate restricts to a surjective continuous map $\sigma(\omega_1 +...

Trait Suggestion: Cohen's modified product S207 is not Connected P36

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## Trait Suggestion Cohen's modified product S207 is not Connected P36. Unknown today https://topology.pi-base.org/spaces/S000207/properties/P000036 ## Proof/References The topology is finer than the product topology on $\omega_1 \times (\omega_1 + 1)$.

Space Suggestion: sigma-product of countably many copies of R

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## Space Suggestion $X$ is the Countable $\sigma$-product $\sigma(\mathbb{R}^\omega)$. I.e., $X$ is the subspace of finitely supported real-valued functions on $\omega$. I.e., $X$ is the subspace of $\mathbb{R}^\omega$ consisting of...