Question

Locally compact metric space

score 4k · Answer 1 · 2016-10-10 18:34:49

4k

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Locally compact metric space

Published on 10 Oct 2016 - 18:34

score 295 · Answer 2 · 2016-10-11 08:57:54

295

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Compactness in weak topology

Published on 11 Oct 2016 - 8:57

score 2.8k · Answer 3 · 2026-03-14 10:52:08

2.8k

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Upper semicontinuous function attains its supremum

Published on 14 Mar 2026 - 10:52

score 2.6k · Answer 4 · 2026-03-26 23:11:31

2.6k

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$\epsilon$-cover of a compact metric space

Published on 26 Mar 2026 - 23:11

score 999 · Answer 5 · 2016-10-11 21:14:17

999

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Differences between extended metric space and metric space

Published on 11 Oct 2016 - 21:14

score 722 · Answer 6 · 2016-10-12 21:13:46

722

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Why is any unbounded subset of the reals not compact?

Published on 12 Oct 2016 - 21:13

score 207 · Answer 7 · 2016-10-13 17:11:12

Is $\prod_{n=1}^{\infty} A_{n}$ with product topology, where $A_{n}$=${\{0,1\}}$ has discrete topology for , $n = 1,2,3,\cdots.$ a compact set?

score 27 · Answer 8 · 2016-10-13 17:12:28

27

Views

$D$ is compact, $U_{1},...,U_{n}$ are open, cover $D$ , then $\exists\delta>0$ s.t $\forall$ $x,y\in D $ with $|x-y|<\delta$, $x,y\in U_{j} $

Published on 13 Oct 2016 - 17:12

score 477 · Answer 9 · 2016-10-16 09:19:54

477

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Why compact subsets (of metric spaces) are closed

Published on 16 Oct 2016 - 9:19

score 202 · Answer 10 · 2016-10-16 14:25:21

202

Views

Heine–Borel theorem: why is the condition closed and bounded?

Published on 16 Oct 2016 - 14:25

score 139 · Answer 11 · 2026-04-01 10:24:58

139

Views

Maximal open coverings without finite subcoverings and the Axiom of Choice.

Published on 01 Apr 2026 - 10:24

score 118 · Answer 12 · 2016-10-17 17:32:42

118

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About compactness theorem application

Published on 17 Oct 2016 - 17:32

score 1.1k · Answer 13 · 2016-10-17 17:47:08

1.1k

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Prove that $[2,4)$ is not compact.

Published on 17 Oct 2016 - 17:47

score 104 · Answer 14 · 2016-10-18 00:08:08

104

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Is $Tf=\int_0^1\alpha (x)f(x)dx$ a compact operator?

Published on 18 Oct 2016 - 0:08

score 89 · Answer 15 · 2016-10-19 20:15:46

89

Views

Why does this proof show that a compact metric space contains a countable subset that the closure of the subset is equal to the whole metric space?

Published on 19 Oct 2016 - 20:15

List Question

Locally compact metric space

Compactness in weak topology

Upper semicontinuous function attains its supremum

$\epsilon$-cover of a compact metric space

Differences between extended metric space and metric space

Why is any unbounded subset of the reals not compact?

Is $\prod_{n=1}^{\infty} A_{n}$ with product topology, where $A_{n}$=${\{0,1\}}$ has discrete topology for , $n = 1,2,3,\cdots.$ a compact set?

$D$ is compact, $U_{1},...,U_{n}$ are open, cover $D$ , then $\exists\delta>0$ s.t $\forall$ $x,y\in D $ with $|x-y|<\delta$, $x,y\in U_{j} $

Why compact subsets (of metric spaces) are closed

Heine–Borel theorem: why is the condition closed and bounded?

Maximal open coverings without finite subcoverings and the Axiom of Choice.

About compactness theorem application

Prove that $[2,4)$ is not compact.

Is $Tf=\int_0^1\alpha (x)f(x)dx$ a compact operator?

Why does this proof show that a compact metric space contains a countable subset that the closure of the subset is equal to the whole metric space?

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