Question

Why "any covering of a compact set by a collection of open sets contains a finite subcovering"?

score 1.3k · Answer 1 · 2018-09-24 16:23:09

1.3k

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Why "any covering of a compact set by a collection of open sets contains a finite subcovering"?

Published on 24 Sep 2018 - 16:23

score 759 · Answer 2 · 2026-03-27 07:02:59

759

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Show that $\text{SO}(2)$ is compact.

Published on 27 Mar 2026 - 7:02

score 454 · Answer 3 · 2018-09-25 12:15:25

454

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Bound on the covering number of a closed ball

Published on 25 Sep 2018 - 12:15

score 1.1k · Answer 4 · 2026-03-25 11:42:07

1.1k

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Prob. 8, Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A map into a compact Hausdorff space is continuous iff its graph is closed

Published on 25 Mar 2026 - 11:42

score 2.7k · Answer 5 · 2018-09-26 21:32:18

2.7k

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How can a set be closed and bounded but not compact?

Published on 26 Sep 2018 - 21:32

score 1.7k · Answer 6 · 2018-09-27 02:59:49

1.7k

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prove that every infinite subset of compact set H has a limit point (Explanation)

Published on 27 Sep 2018 - 2:59

score 393 · Answer 7 · 2026-03-25 09:53:52

393

Views

Compactness of $PGL(n, \mathbb{R})$ and $PGL(n, \mathbb{C})$

Published on 25 Mar 2026 - 9:53

score 310 · Answer 8 · 2026-03-25 01:33:28

310

Views

Finite Complement Topology, Compactness, and Closedness

Published on 25 Mar 2026 - 1:33

score 90 · Answer 9 · 2018-09-28 01:32:26

90

Views

Compact and convex properties of the set $\{(x,y) \in \mathbb{R}^2 | 1 \leq x^2 + y^2 \leq 2 \}$

Published on 28 Sep 2018 - 1:32

score 120 · Answer 10 · 2018-09-28 19:08:14

120

Views

$(X,d)$ is compact if each $(X,d_k)$ is compact

Published on 28 Sep 2018 - 19:08

score 176 · Answer 11 · 2018-09-28 19:28:51

176

Views

A confusion regarding Closed graph theorem

Published on 28 Sep 2018 - 19:28

score 39 · Answer 12 · 2018-09-29 03:02:51

39

Views

Coordinate continuity and preservation of compactness implying continuity.

Published on 29 Sep 2018 - 3:02

score 314 · Answer 13 · 2018-09-30 20:22:18

314

Views

Sequence Converges to Infinity in a Topological Space

Published on 30 Sep 2018 - 20:22

score 353 · Answer 14 · 2026-03-25 09:48:15

353

Views

Lebesgue outer measure equivalence to another set function on compact sets

Published on 25 Mar 2026 - 9:48

score 1.6k · Answer 15 · 2018-10-02 11:15:00

1.6k

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Prob. 2 (d), Sec. 27, in Munkres' TOPOLOGY, 2nd ed: If $A$ is compact and $U$ is an open set containing $A$, then . . .

Published on 02 Oct 2018 - 11:15

List Question

Why "any covering of a compact set by a collection of open sets contains a finite subcovering"?

Show that $\text{SO}(2)$ is compact.

Bound on the covering number of a closed ball

Prob. 8, Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A map into a compact Hausdorff space is continuous iff its graph is closed

How can a set be closed and bounded but not compact?

prove that every infinite subset of compact set H has a limit point (Explanation)

Compactness of $PGL(n, \mathbb{R})$ and $PGL(n, \mathbb{C})$

Finite Complement Topology, Compactness, and Closedness

Compact and convex properties of the set $\{(x,y) \in \mathbb{R}^2 | 1 \leq x^2 + y^2 \leq 2 \}$

$(X,d)$ is compact if each $(X,d_k)$ is compact

A confusion regarding Closed graph theorem

Coordinate continuity and preservation of compactness implying continuity.

Sequence Converges to Infinity in a Topological Space

Lebesgue outer measure equivalence to another set function on compact sets

Prob. 2 (d), Sec. 27, in Munkres' TOPOLOGY, 2nd ed: If $A$ is compact and $U$ is an open set containing $A$, then . . .

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