Question

$A = \{ \sum_{k=1}^{\infty} a_ke_k :|a_k|\leq c_k \} \subset \mathcal H$ is compact, where $\sum c_k^2<\infty$

score 180 · Answer 1 · 2023-05-27 12:15:58

180

Views

$A = \{ \sum_{k=1}^{\infty} a_ke_k :|a_k|\leq c_k \} \subset \mathcal H$ is compact, where $\sum c_k^2<\infty$

Published on 27 May 2023 - 12:15

score 83 · Answer 2 · 2023-05-30 08:36:20

83

Views

Do $X$ and $kX$ have the same compact subsets only if $X$ is weak Hausdorff?

Published on 30 May 2023 - 8:36

score 50 · Answer 3 · 2026-03-26 14:24:55

50

Views

Locally compact and regular topogical space needs to be Hausdorff?

Published on 26 Mar 2026 - 14:24

score 210 · Answer 4 · 2023-05-31 19:19:33

210

Views

If every continuous real-valued function defined on K is bounded, then K is compact?

Published on 31 May 2023 - 19:19

score 50 · Answer 5 · 2023-06-05 14:14:01

50

Views

Does this proof of the compactness theorem assumes countable atomic formulas?

Published on 05 Jun 2023 - 14:14

score 36 · Answer 6 · 2023-06-06 08:16:54

36

Views

Compactness of Sets of Probability Measures on countable space

Published on 06 Jun 2023 - 8:16

score 153 · Answer 7 · 2026-04-08 09:31:12

153

Views

What is the relationship between ultrafilters and propositional theories?

Published on 08 Apr 2026 - 9:31

score 97 · Answer 8 · 2023-06-09 12:02:11

97

Views

Given continuous $f:\mathbb{R}\to\mathbb{R}$ and compact $K\subseteq f(\mathbb{R})$, show there exists a compact set $C$ such that $f(C)=K$.

Published on 09 Jun 2023 - 12:02

score 48 · Answer 9 · 2026-04-09 01:59:06

48

Views

Confusion about Compact Set Example of Topology

Published on 09 Apr 2026 - 1:59

score 19 · Answer 10 · 2026-03-28 21:44:21

19

Views

sufficient and necessary condition to change the order of minimization (infimum)

Published on 28 Mar 2026 - 21:44

score 119 · Answer 11 · 2023-06-12 13:05:42

119

Views

The Lindelöf space of $\mathbb{R}^n$.

Published on 12 Jun 2023 - 13:05

score 53 · Answer 12 · 2023-06-13 10:54:48

53

Views

$\sigma$-compact space of $\mathbb{R}^n$.

Published on 13 Jun 2023 - 10:54

score 44 · Answer 13 · 2023-06-14 08:59:25

44

Views

Is C(R) compact space in regard to given metric

Published on 14 Jun 2023 - 8:59

score 79 · Answer 14 · 2026-04-06 20:44:08

79

Views

Counterexample: locally compact non-Hausdorff space where open sets are sigma-compact and compact sets are closed?

Published on 06 Apr 2026 - 20:44

score 50 · Answer 15 · 2026-02-23 04:57:24

50

Views

Can every open set of a polish space be expressed as a countable union of compact sets?

Published on 23 Feb 2026 - 4:57

List Question

$A = \{ \sum_{k=1}^{\infty} a_ke_k :|a_k|\leq c_k \} \subset \mathcal H$ is compact, where $\sum c_k^2<\infty$

Do $X$ and $kX$ have the same compact subsets only if $X$ is weak Hausdorff?

Locally compact and regular topogical space needs to be Hausdorff?

If every continuous real-valued function defined on K is bounded, then K is compact?

Does this proof of the compactness theorem assumes countable atomic formulas?

Compactness of Sets of Probability Measures on countable space

What is the relationship between ultrafilters and propositional theories?

Given continuous $f:\mathbb{R}\to\mathbb{R}$ and compact $K\subseteq f(\mathbb{R})$, show there exists a compact set $C$ such that $f(C)=K$.

Confusion about Compact Set Example of Topology

sufficient and necessary condition to change the order of minimization (infimum)

The Lindelöf space of $\mathbb{R}^n$.

$\sigma$-compact space of $\mathbb{R}^n$.

Is C(R) compact space in regard to given metric

Counterexample: locally compact non-Hausdorff space where open sets are sigma-compact and compact sets are closed?

Can every open set of a polish space be expressed as a countable union of compact sets?

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