List questions from separation-axioms

Published on 29 Oct 2016 - 14:18

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Every $\sigma$-compact LCH space is para-compact

Published on 07 Nov 2016 - 1:10

329

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If $X$ and $Y$ are Hausdorff, $X$ is compact, and $f:X\to Y$ is continuous and surjective, then $f$ is open.

Published on 08 Nov 2016 - 7:54

322

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Closure of range of a compact operator is separable

Published on 13 Nov 2016 - 10:57

251

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If a space is regular and every point has a compact neighborhood, is it locally compact?

Published on 19 Nov 2016 - 9:33

6.7k

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Prove that a regular Lindelöf topological space is normal

Published on 23 Nov 2016 - 12:12

359

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T_{0} space with clopen base is totally disconnected

Published on 23 Nov 2016 - 20:22

268

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If a regular space is a countable union of compact subspaces then is it paracompact?

Published on 23 Feb 2026 - 2:39

755

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Does the union of two Hausdorff subspaces Hausdorff in this case?

Published on 25 Nov 2016 - 21:32

70

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Why is $Y$ Hausdorff in this proof?

Published on 27 Nov 2016 - 20:54

1.6k

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Help understanding proof of every topological group is regular

Published on 01 Dec 2016 - 15:35

795

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Let $p: X \to Y$ be a perfect map. Show that if $X$ is regular, $Y$ is regular.

Published on 04 Dec 2016 - 3:13

700

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Is the projection on a product topology surjective?

Published on 06 Dec 2016 - 1:50

157

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Three closed sets in $T_4$ space which have an empty intersection.

Published on 06 Dec 2016 - 12:36

746

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Why is $\mathbb{R}/(-1,1)$ not Hausdorff?

Published on 15 Dec 2016 - 2:25

List Question

Example of a $T_0$ and normal that is not $T_4$

Every $\sigma$-compact LCH space is para-compact

If $X$ and $Y$ are Hausdorff, $X$ is compact, and $f:X\to Y$ is continuous and surjective, then $f$ is open.

Closure of range of a compact operator is separable

If a space is regular and every point has a compact neighborhood, is it locally compact?

Prove that a regular Lindelöf topological space is normal

T_{0} space with clopen base is totally disconnected

If a regular space is a countable union of compact subspaces then is it paracompact?

Does the union of two Hausdorff subspaces Hausdorff in this case?

Why is $Y$ Hausdorff in this proof?

Help understanding proof of every topological group is regular

Let $p: X \to Y$ be a perfect map. Show that if $X$ is regular, $Y$ is regular.

Is the projection on a product topology surjective?

Three closed sets in $T_4$ space which have an empty intersection.

Why is $\mathbb{R}/(-1,1)$ not Hausdorff?

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