Question

Question about an open cover of (0,1]

score 84 · Answer 1 · 2018-05-15 22:26:22

84

Views

Question about an open cover of (0,1]

Published on 15 May 2018 - 22:26

score 73 · Answer 2 · 2018-05-16 05:44:57

73

Views

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

Published on 16 May 2018 - 5:44

score 1k · Answer 3 · 2018-05-16 06:03:08

1k

Views

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

Published on 16 May 2018 - 6:03

score 320 · Answer 4 · 2018-05-17 06:42:53

320

Views

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

Published on 17 May 2018 - 6:42

score 31 · Answer 5 · 2018-05-17 20:29:11

31

Views

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

Published on 17 May 2018 - 20:29

score 476 · Answer 6 · 2018-05-17 21:22:47

476

Views

Proving one compactness theorem from the other

Published on 17 May 2018 - 21:22

score 921 · Answer 7 · 2018-05-17 23:57:07

921

Views

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

Published on 17 May 2018 - 23:57

score 106 · Answer 8 · 2018-05-18 10:42:25

106

Views

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 18 May 2018 - 10:42

score 47 · Answer 9 · 2018-05-18 13:36:11

47

Views

How do I show that the set is compact?

Published on 18 May 2018 - 13:36

score 125 · Answer 10 · 2018-05-18 15:58:04

125

Views

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

Published on 18 May 2018 - 15:58

score 345 · Answer 11 · 2026-03-25 19:00:44

345

Views

Alexandroff compactification topology

Published on 25 Mar 2026 - 19:00

score 46 · Answer 12 · 2018-05-19 16:34:19

46

Views

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

Published on 19 May 2018 - 16:34

score 87 · Answer 13 · 2018-05-19 22:08:59

87

Views

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

Published on 19 May 2018 - 22:08

score 1.7k · Answer 14 · 2026-03-25 08:00:38

1.7k

Views

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

Published on 25 Mar 2026 - 8:00

score 855 · Answer 15 · 2026-03-25 19:04:39

855

Views

Example of positive measure compact set that contains no interval.

Published on 25 Mar 2026 - 19:04

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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