Question

Why is compactness important to find solution of certain problems?

score 222 · Answer 1 · 2026-05-14 17:09:16

Why is compactness important to find solution of certain problems?

Published on 14 May 2026 - 17:09

score 57 · Answer 2 · 2026-05-14 17:14:02

$K = \{A \in \Bbb M_n (\Bbb R)\ |\ A=A^T, \mathrm {tr} (A) = 1, x^TAx \ge 0\ \text {for all}\ x \in \Bbb R^n \}$ is compact or not?

score 156 · Answer 3 · 2026-05-10 15:15:21

156

Views

Compactness in weak$^*$-topology on $l_1(\mathbb{N})$

Published on 10 May 2026 - 15:15

score 56 · Answer 4 · 2026-05-11 03:12:58

56

Views

Rudin's functional analysis appendix A4 (a)

Published on 11 May 2026 - 3:12

score 95 · Answer 5 · 2026-04-11 02:46:20

95

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An alternative definition of compact sets

Published on 11 Apr 2026 - 2:46

score 621 · Answer 6 · 2026-05-14 18:22:55

621

Views

Prove weighted ball in $l^2$ space is compact

Published on 14 May 2026 - 18:22

score 98 · Answer 7 · 2026-05-14 14:25:12

98

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Possible use of choice in proving "Compactness implies limit point compactness"

Published on 14 May 2026 - 14:25

score 45 · Answer 8 · 2026-04-12 00:48:58

45

Views

What's the reason that exponentials are often used when requiring compact support?

Published on 12 Apr 2026 - 0:48

score 63 · Answer 9 · 2026-05-10 20:33:09

63

Views

Questions about Tychonoff spaces natural embedding.

Published on 10 May 2026 - 20:33

score 132 · Answer 10 · 2026-05-10 20:33:00

132

Views

Is $[0,1]^A$ not sequentially compact for any uncountable $A$?

Published on 10 May 2026 - 20:33

score 160 · Answer 11 · 2026-05-10 17:13:51

160

Views

Question regarding proof of Tychonoff's theorem

Published on 10 May 2026 - 17:13

score 218 · Answer 12 · 2026-05-14 22:05:57

218

Views

Does adding a continuous inequality constraint over a compact set lead to another compact set?

Published on 14 May 2026 - 22:05

score 66 · Answer 13 · 2026-04-14 04:50:41

66

Views

Isometry $f:M\mapsto M$ is surjective if $M$ is compact: proof by composing $f$ with itself

Published on 14 Apr 2026 - 4:50

score 191 · Answer 14 · 2026-04-15 20:58:08

191

Views

Showing that $f:M\mapsto M$ has a unique fixed point if $M$ is compact and $d(f(a),f(b))<d(a,b)~\forall a,b\in M$

Published on 15 Apr 2026 - 20:58

score 122 · Answer 15 · 2026-05-14 22:09:39

122

Views

Strategy to prove a set is compact. Case: $S=\{0\}\cup\bigcup_\limits{i=1}^{\infty}\{\frac{1}{n}\}$

Published on 14 May 2026 - 22:09

List Question

Why is compactness important to find solution of certain problems?

$K = \{A \in \Bbb M_n (\Bbb R)\ |\ A=A^T, \mathrm {tr} (A) = 1, x^TAx \ge 0\ \text {for all}\ x \in \Bbb R^n \}$ is compact or not?

Compactness in weak$^*$-topology on $l_1(\mathbb{N})$

Rudin's functional analysis appendix A4 (a)

An alternative definition of compact sets

Prove weighted ball in $l^2$ space is compact

Possible use of choice in proving "Compactness implies limit point compactness"

What's the reason that exponentials are often used when requiring compact support?

Questions about Tychonoff spaces natural embedding.

Is $[0,1]^A$ not sequentially compact for any uncountable $A$?

Question regarding proof of Tychonoff's theorem

Does adding a continuous inequality constraint over a compact set lead to another compact set?

Isometry $f:M\mapsto M$ is surjective if $M$ is compact: proof by composing $f$ with itself

Showing that $f:M\mapsto M$ has a unique fixed point if $M$ is compact and $d(f(a),f(b))<d(a,b)~\forall a,b\in M$

Strategy to prove a set is compact. Case: $S=\{0\}\cup\bigcup_\limits{i=1}^{\infty}\{\frac{1}{n}\}$

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