Question

Do locally compact Hausdorff spaces and proper maps as morphisms form a category?

score 192 · Answer 1 · 2026-03-29 16:14:20

192

Views

Do locally compact Hausdorff spaces and proper maps as morphisms form a category?

Published on 29 Mar 2026 - 16:14

score 98 · Answer 2 · 2022-06-21 08:00:14

98

Views

$X$ is $T_1$, compact and extremally disconnected, then $X$ is 0-dimensional

Published on 21 Jun 2022 - 8:00

score 27 · Answer 3 · 2026-02-23 06:16:35

27

Views

Tychonoff spaces and separating points.

Published on 23 Feb 2026 - 6:16

score 89 · Answer 4 · 2026-03-26 13:01:04

89

Views

Does there exists any locally compact haussdoff space $(X, \tau) $ which is totally disconnected but not zero dimensional?

Published on 26 Mar 2026 - 13:01

score 268 · Answer 5 · 2026-03-26 09:37:29

268

Views

Source to "Strongly zero-dimensional and zero-dimensional is equivalent for separable metrizable spaces"?

Published on 26 Mar 2026 - 9:37

score 158 · Answer 6 · 2022-07-24 09:11:19

158

Views

Do locally compact Hausdorff spaces admit local bases consisting of normal open neighbourhoods?

Published on 24 Jul 2022 - 9:11

score 98 · Answer 7 · 2022-07-28 15:59:24

98

Views

If $X$ is perfectly normal then for any closed set there exists a continuous function $φ:X⟶[0,1]$ such that $φ^{-1}[0]=C$ and $φ^{-1}[1]=∅$.

Published on 28 Jul 2022 - 15:59

score 224 · Answer 8 · 2022-08-04 17:07:58

224

Views

Prove that any topological group is completely regular.

Published on 04 Aug 2022 - 17:07

score 48 · Answer 9 · 2022-08-09 06:23:07

48

Views

Proving (directly) the equivalence between two definitions of a Fréchet or $T_1$ space.

Published on 09 Aug 2022 - 6:23

score 59 · Answer 10 · 2022-08-16 17:08:23

59

Views

When does Limit-point compactness imply compactness or sequential compactness?

Published on 16 Aug 2022 - 17:08

score 115 · Answer 11 · 2022-09-05 07:05:14

115

Views

Perfectly normal spaces are completely regular

Published on 05 Sep 2022 - 7:05

score 147 · Answer 12 · 2022-09-08 23:33:18

147

Views

$X$ is completely regular if and only if the zero set nbhds of each point form a nbhd base

Published on 08 Sep 2022 - 23:33

score 41 · Answer 13 · 2022-09-10 22:29:54

41

Views

Prove that a countable completely regular space is zero dimensional

Published on 10 Sep 2022 - 22:29

score 40 · Answer 14 · 2026-02-23 06:25:22

40

Views

If $f(A)$ and $f(B)$ are separated by neighborhoods in $\mathbb R$, are $A$ and $B$ separated by a function?

Published on 23 Feb 2026 - 6:25

score 75 · Answer 15 · 2026-02-23 06:25:20

75

Views

If $f(x)$ and $f(C)$ are separated by neighborhoods in $\mathbb R$, are $x$ and $C$ separated by a function?

Published on 23 Feb 2026 - 6:25

List Question

Do locally compact Hausdorff spaces and proper maps as morphisms form a category?

$X$ is $T_1$, compact and extremally disconnected, then $X$ is 0-dimensional

Tychonoff spaces and separating points.

Does there exists any locally compact haussdoff space $(X, \tau) $ which is totally disconnected but not zero dimensional?

Source to "Strongly zero-dimensional and zero-dimensional is equivalent for separable metrizable spaces"?

Do locally compact Hausdorff spaces admit local bases consisting of normal open neighbourhoods?

If $X$ is perfectly normal then for any closed set there exists a continuous function $φ:X⟶[0,1]$ such that $φ^{-1}[0]=C$ and $φ^{-1}[1]=∅$.

Prove that any topological group is completely regular.

Proving (directly) the equivalence between two definitions of a Fréchet or $T_1$ space.

When does Limit-point compactness imply compactness or sequential compactness?

Perfectly normal spaces are completely regular

$X$ is completely regular if and only if the zero set nbhds of each point form a nbhd base

Prove that a countable completely regular space is zero dimensional

If $f(A)$ and $f(B)$ are separated by neighborhoods in $\mathbb R$, are $A$ and $B$ separated by a function?

If $f(x)$ and $f(C)$ are separated by neighborhoods in $\mathbb R$, are $x$ and $C$ separated by a function?

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