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Question about the proof of "If K is a compact set of the metric space Ω, then K is closed"

score 288 · Answer 1 · 2016-12-03 22:04:13

288

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Question about the proof of "If K is a compact set of the metric space Ω, then K is closed"

Published on 03 Dec 2016 - 22:04

score 85 · Answer 2 · 2016-12-04 09:39:07

85

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What do you call a topology where every open set is compact?

Published on 04 Dec 2016 - 9:39

score 115 · Answer 3 · 2016-12-05 01:36:50

115

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Spaces on which every continuous one-to-one map is a homeomorphism

Published on 05 Dec 2016 - 1:36

score 65 · Answer 4 · 2016-12-05 03:08:36

65

Views

Let $T$ extend the theory of Groups. Prove there is a bound to the order.

Published on 05 Dec 2016 - 3:08

score 497 · Answer 5 · 2026-02-23 13:47:47

497

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Generalized theorem of Arzela Ascoli

Published on 23 Feb 2026 - 13:47

score 1.2k · Answer 6 · 2016-12-05 20:35:45

1.2k

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Examples about maximal Abelian subgroup is not a maximal torus in compact connected Lie group $G$.

Published on 05 Dec 2016 - 20:35

score 49 · Answer 7 · 2016-12-06 01:41:41

49

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$\int_a^bf(x) dx=\int_a^bf^\prime(x) dx$

Published on 06 Dec 2016 - 1:41

score 156 · Answer 8 · 2016-12-06 05:51:43

156

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Is this a compact (closed + bounded) set of vectors in $\mathbb R^n$?

Published on 06 Dec 2016 - 5:51

score 41 · Answer 9 · 2016-12-06 13:51:36

41

Views

Compact mapping from $C([0,1])$ to itself.

Published on 06 Dec 2016 - 13:51

score 714 · Answer 10 · 2016-12-06 22:18:36

714

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If $h:X \to Y$ is a homeomorphism of metric spaces, how do I prove that $X$ is compact if and only if $Y$ is compact?

Published on 06 Dec 2016 - 22:18

score 1k · Answer 11 · 2016-12-07 11:15:00

1k

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If for every cover of open balls there exists a finite sub-cover, then $K$ is sequentially compact

Published on 07 Dec 2016 - 11:15

score 119 · Answer 12 · 2016-12-07 17:23:42

119

Views

Are filters compact?

Published on 07 Dec 2016 - 17:23

score 7.8k · Answer 13 · 2016-12-09 03:44:40

7.8k

Views

Show that $\mathbb{R}$, when equipped with the standard topology, is not compact.

Published on 09 Dec 2016 - 3:44

score 110 · Answer 14 · 2016-12-10 14:22:59

110

Views

Compactness of a set in a metric space

Published on 10 Dec 2016 - 14:22

score 85 · Answer 15 · 2016-12-10 16:06:11

85

Views

Prove that a point is always in the interior of a compact

Published on 10 Dec 2016 - 16:06

List Question

Question about the proof of "If K is a compact set of the metric space Ω, then K is closed"

What do you call a topology where every open set is compact?

Spaces on which every continuous one-to-one map is a homeomorphism

Let $T$ extend the theory of Groups. Prove there is a bound to the order.

Generalized theorem of Arzela Ascoli

Examples about maximal Abelian subgroup is not a maximal torus in compact connected Lie group $G$.

$\int_a^bf(x) dx=\int_a^bf^\prime(x) dx$

Is this a compact (closed + bounded) set of vectors in $\mathbb R^n$?

Compact mapping from $C([0,1])$ to itself.

If $h:X \to Y$ is a homeomorphism of metric spaces, how do I prove that $X$ is compact if and only if $Y$ is compact?

If for every cover of open balls there exists a finite sub-cover, then $K$ is sequentially compact

Are filters compact?

Show that $\mathbb{R}$, when equipped with the standard topology, is not compact.

Compactness of a set in a metric space

Prove that a point is always in the interior of a compact

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