Question

Are boundedly compact metric space always equal to a countable union of their compact subsets?

score 93 · Answer 1 · 2020-01-31 18:32:52

93

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Are boundedly compact metric space always equal to a countable union of their compact subsets?

Published on 31 Jan 2020 - 18:32

score 236 · Answer 2 · 2020-02-02 16:54:38

236

Views

Precision Regarding Proposition 1.15 in Folland's Real Analysis

Published on 02 Feb 2020 - 16:54

score 57 · Answer 3 · 2020-02-02 17:20:28

57

Views

What is the exact definition of compactness

Published on 02 Feb 2020 - 17:20

score 46 · Answer 4 · 2026-03-26 01:01:20

46

Views

Compact Hausdorff space and closure

Published on 26 Mar 2026 - 1:01

score 705 · Answer 5 · 2020-02-02 21:25:09

705

Views

If $K$ is a compact subset of $\mathbb{R}^d$, then $K$ contains a point of maximal norm.

Published on 02 Feb 2020 - 21:25

score 109 · Answer 6 · 2026-03-25 20:58:02

109

Views

How do I prove this topological space is T2 and compact?

Published on 25 Mar 2026 - 20:58

score 27 · Answer 7 · 2020-02-04 21:30:04

27

Views

Subsets of a fixed cardinality are open or closed in the product topology $\{0,1\}^{\mathbb{N}}$

Published on 04 Feb 2020 - 21:30

score 106 · Answer 8 · 2020-02-05 22:50:17

106

Views

Compact metric space: distance from any given point.

Published on 05 Feb 2020 - 22:50

score 129 · Answer 9 · 2020-02-06 01:11:34

129

Views

Extracting a finite subcover from a countable subcover for a compact set

Published on 06 Feb 2020 - 1:11

score 70 · Answer 10 · 2020-02-06 21:32:14

70

Views

Is $E=\{(x,y) \in \mathbb R^2 | y^2-xy-x^3=0\}$ compact?

Published on 06 Feb 2020 - 21:32

score 124 · Answer 11 · 2020-02-07 21:30:02

124

Views

Need help understanding why my proof that [0,1] is compact is wrong?

Published on 07 Feb 2020 - 21:30

score 96 · Answer 12 · 2020-02-10 20:44:10

96

Views

Wrong counterexample to $[0,1]^\omega$ with product topology being not limit point compact

Published on 10 Feb 2020 - 20:44

score 201 · Answer 13 · 2026-03-28 11:33:36

201

Views

Why isn't $B = \{x \in l_{\infty} : \| x \|_{\infty} \leq 1 \}$ a compact metric space?

Published on 28 Mar 2026 - 11:33

score 211 · Answer 14 · 2020-02-13 23:06:27

211

Views

Compact subset of a finite dimensional inner product space

Published on 13 Feb 2020 - 23:06

score 966 · Answer 15 · 2026-03-25 12:53:57

966

Views

$X$ is compact iff every net in $X$ has a convergent subnet (using filters).

Published on 25 Mar 2026 - 12:53

List Question

Are boundedly compact metric space always equal to a countable union of their compact subsets?

Precision Regarding Proposition 1.15 in Folland's Real Analysis

What is the exact definition of compactness

Compact Hausdorff space and closure

If $K$ is a compact subset of $\mathbb{R}^d$, then $K$ contains a point of maximal norm.

How do I prove this topological space is T2 and compact?

Subsets of a fixed cardinality are open or closed in the product topology $\{0,1\}^{\mathbb{N}}$

Compact metric space: distance from any given point.

Extracting a finite subcover from a countable subcover for a compact set

Is $E=\{(x,y) \in \mathbb R^2 | y^2-xy-x^3=0\}$ compact?

Need help understanding why my proof that [0,1] is compact is wrong?

Wrong counterexample to $[0,1]^\omega$ with product topology being not limit point compact

Why isn't $B = \{x \in l_{\infty} : \| x \|_{\infty} \leq 1 \}$ a compact metric space?

Compact subset of a finite dimensional inner product space

$X$ is compact iff every net in $X$ has a convergent subnet (using filters).

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