Question

Are any open subsets of $\mathbb{R}^N$ $ \sigma$ -compact?

score 113 · Answer 1 · 2023-08-30 08:19:35

113

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Are any open subsets of $\mathbb{R}^N$ $ \sigma$ -compact?

Published on 30 Aug 2023 - 8:19

score 79 · Answer 2 · 2026-04-05 23:03:05

79

Views

Compact vs. Linearly Compact

Published on 05 Apr 2026 - 23:03

score 45 · Answer 3 · 2026-03-26 16:05:15

45

Views

Are retracts always closed in a compact weak Hausdorff space?

Published on 26 Mar 2026 - 16:05

score 130 · Answer 4 · 2023-09-02 08:07:34

130

Views

Measures of noncompactness in locally convex topological vector spaces

Published on 02 Sep 2023 - 8:07

score 22 · Answer 5 · 2023-09-03 05:09:15

22

Views

$L_p$ space for a compact Hausdorff group

Published on 03 Sep 2023 - 5:09

score 128 · Answer 6 · 2026-04-07 03:09:27

128

Views

If $\varphi : X\times Y\rightarrow Z$ is continuous, $\widehat{\varphi} : X\rightarrow C(Y,Z)$ is not necessary continuous.

Published on 07 Apr 2026 - 3:09

score 69 · Answer 7 · 2023-09-07 19:51:44

69

Views

In a complete locally compact length metric space there exists an open ball between a given compact ball and an open set containing it (Hopf-Rinow)

Published on 07 Sep 2023 - 19:51

score 41 · Answer 8 · 2023-09-09 22:51:14

41

Views

Showing compactness of the space $\{-1, 1\}^{\mathbb{N}}$ using diagonal argument

Published on 09 Sep 2023 - 22:51

score 82 · Answer 9 · 2023-09-11 18:58:11

82

Views

Hilbert-Schmidt norm on direct sums of Hilbert spaces

Published on 11 Sep 2023 - 18:58

score 61 · Answer 10 · 2026-03-25 10:55:50

61

Views

Reverse mathematics of characterization of compact spaces

Published on 25 Mar 2026 - 10:55

score 111 · Answer 11 · 2023-09-15 12:39:58

111

Views

Every co-finite topology is compact?

Published on 15 Sep 2023 - 12:39

score 67 · Answer 12 · 2023-09-18 10:31:40

67

Views

If $f_n\nearrow f$ pointwise monotone on a compact set $C$, does $\inf f_n(C) \to \inf f(C)$?

Published on 18 Sep 2023 - 10:31

score 73 · Answer 13 · 2023-09-19 22:17:59

73

Views

Which of these interpretations of "relatively compact" does Rudin mean in Baby Rudin?

Published on 19 Sep 2023 - 22:17

score 71 · Answer 14 · 2026-03-28 07:58:43

71

Views

Rudin's proof about closed subsets of compact sets

Published on 28 Mar 2026 - 7:58

score 36 · Answer 15 · 2023-09-21 19:12:18

36

Views

Compactness of operator $T_K(f)(s) = \int_0^1 K(t,s) f(t)\,{\rm d}t.$

Published on 21 Sep 2023 - 19:12

List Question

Are any open subsets of $\mathbb{R}^N$ $ \sigma$ -compact?

Compact vs. Linearly Compact

Are retracts always closed in a compact weak Hausdorff space?

Measures of noncompactness in locally convex topological vector spaces

$L_p$ space for a compact Hausdorff group

If $\varphi : X\times Y\rightarrow Z$ is continuous, $\widehat{\varphi} : X\rightarrow C(Y,Z)$ is not necessary continuous.

In a complete locally compact length metric space there exists an open ball between a given compact ball and an open set containing it (Hopf-Rinow)

Showing compactness of the space $\{-1, 1\}^{\mathbb{N}}$ using diagonal argument

Hilbert-Schmidt norm on direct sums of Hilbert spaces

Reverse mathematics of characterization of compact spaces

Every co-finite topology is compact?

If $f_n\nearrow f$ pointwise monotone on a compact set $C$, does $\inf f_n(C) \to \inf f(C)$?

Which of these interpretations of "relatively compact" does Rudin mean in Baby Rudin?

Rudin's proof about closed subsets of compact sets

Compactness of operator $T_K(f)(s) = \int_0^1 K(t,s) f(t)\,{\rm d}t.$

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