Question

Question about an open cover of (0,1]

score 87 · Answer 1 · 2026-04-11 23:12:06

87

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Question about an open cover of (0,1]

Published on 11 Apr 2026 - 23:12

score 76 · Answer 2 · 2026-04-11 02:32:31

76

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Does a closed subset bounded away from boundary in the subspace topology imply compactness?

Published on 11 Apr 2026 - 2:32

score 1k · Answer 3 · 2026-04-16 19:33:12

1k

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If $K$ compact then $K$ is closed (a proof by sequences)

Published on 16 Apr 2026 - 19:33

score 323 · Answer 4 · 2026-04-11 00:22:42

323

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Is every open subset of a locally compact Hausdorff space, locally compact in the subspace topology?

Published on 11 Apr 2026 - 0:22

score 34 · Answer 5 · 2026-04-11 02:07:24

34

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Closed subsets of a compact topological space are compact proof clarification 3

Published on 11 Apr 2026 - 2:07

score 479 · Answer 6 · 2026-04-15 03:32:20

479

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Proving one compactness theorem from the other

Published on 15 Apr 2026 - 3:32

score 924 · Answer 7 · 2026-04-14 22:23:09

924

Views

Any open or closed subset of a locally compact space is also locally compact

Published on 14 Apr 2026 - 22:23

score 109 · Answer 8 · 2026-04-16 14:18:49

109

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If $B \subset \mathbb R^m$ is compact and $x\in \mathbb R^n$ then $\{x\} \times B \subset \mathbb R^{n+m}$ is compact.

Published on 16 Apr 2026 - 14:18

score 50 · Answer 9 · 2026-04-09 21:39:42

50

Views

How do I show that the set is compact?

Published on 09 Apr 2026 - 21:39

score 128 · Answer 10 · 2026-04-11 06:54:21

128

Views

How do I show that this set is compact and not compact at the same time?

Published on 11 Apr 2026 - 6:54

score 351 · Answer 11 · 2026-05-13 00:34:27

351

Views

Alexandroff compactification topology

Published on 13 May 2026 - 0:34

score 49 · Answer 12 · 2026-04-16 00:51:52

49

Views

$\left[0,1\right]$ can be covered with a finite number of "small" intervals

Published on 16 Apr 2026 - 0:51

score 90 · Answer 13 · 2026-04-16 08:56:03

90

Views

$H = [1,\infty)$ with $d(x,y) = |\frac{1}{x} - \frac{1}{y}|$ is not Compact by covers

Published on 16 Apr 2026 - 8:56

score 1.7k · Answer 14 · 2026-05-10 13:25:52

1.7k

Views

Show that if $X$ is locally compact and $\sigma$-compact then is separable

Published on 10 May 2026 - 13:25

score 858 · Answer 15 · 2026-05-10 16:11:40

858

Views

Example of positive measure compact set that contains no interval.

Published on 10 May 2026 - 16:11

List Question

Question about an open cover of (0,1]

Does a closed subset bounded away from boundary in the subspace topology imply compactness?

If $K$ compact then $K$ is closed (a proof by sequences)

Is every open subset of a locally compact Hausdorff space, locally compact in the subspace topology?

Closed subsets of a compact topological space are compact proof clarification 3

Proving one compactness theorem from the other

Any open or closed subset of a locally compact space is also locally compact

If $B \subset \mathbb R^m$ is compact and $x\in \mathbb R^n$ then $\{x\} \times B \subset \mathbb R^{n+m}$ is compact.

How do I show that the set is compact?

How do I show that this set is compact and not compact at the same time?

Alexandroff compactification topology

$\left[0,1\right]$ can be covered with a finite number of "small" intervals

$H = [1,\infty)$ with $d(x,y) = |\frac{1}{x} - \frac{1}{y}|$ is not Compact by covers

Show that if $X$ is locally compact and $\sigma$-compact then is separable

Example of positive measure compact set that contains no interval.

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