Question

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

score 1.3k · Answer 1 · 2026-04-14 18:40:59

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 14 Apr 2026 - 18:40

score 762 · Answer 2 · 2026-05-10 14:50:28

762

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

Published on 10 May 2026 - 14:50

score 457 · Answer 3 · 2026-04-16 08:36:10

457

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Bound on the covering number of a closed ball

Published on 16 Apr 2026 - 8:36

score 1.1k · Answer 4 · 2026-05-13 17:51:33

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 13 May 2026 - 17:51

score 2.7k · Answer 5 · 2026-04-08 23:08:59

2.7k

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

Published on 08 Apr 2026 - 23:08

score 1.7k · Answer 6 · 2026-04-09 00:14:58

1.7k

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

Published on 09 Apr 2026 - 0:14

score 396 · Answer 7 · 2026-05-11 06:39:40

396

Views

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

Published on 11 May 2026 - 6:39

score 313 · Answer 8 · 2026-05-10 14:58:21

313

Views

Finite Complement Topology, Compactness, and Closedness

Published on 10 May 2026 - 14:58

score 93 · Answer 9 · 2026-04-14 23:23:12

93

Views

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

Published on 14 Apr 2026 - 23:23

score 123 · Answer 10 · 2026-04-15 02:23:54

123

Views

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

Published on 15 Apr 2026 - 2:23

score 179 · Answer 11 · 2026-04-14 07:33:57

179

Views

A confusion regarding Closed graph theorem

Published on 14 Apr 2026 - 7:33

score 42 · Answer 12 · 2026-04-12 07:31:32

42

Views

Coordinate continuity and preservation of compactness implying continuity.

Published on 12 Apr 2026 - 7:31

score 317 · Answer 13 · 2026-04-15 13:13:23

317

Views

Sequence Converges to Infinity in a Topological Space

Published on 15 Apr 2026 - 13:13

score 356 · Answer 14 · 2026-05-10 14:47:52

356

Views

Lebesgue outer measure equivalence to another set function on compact sets

Published on 10 May 2026 - 14:47

score 1.6k · Answer 15 · 2026-04-16 15:50:09

1.6k

Views

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 16 Apr 2026 - 15:50

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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