Question

Proving that $\mathbb{R}^ω$ is not $\sigma$-compact.

score 58 · Answer 1 · 2023-12-25 09:34:25

58

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Proving that $\mathbb{R}^ω$ is not $\sigma$-compact.

Published on 25 Dec 2023 - 9:34

score 64 · Answer 2 · 2023-12-29 20:36:46

64

Views

complete metric space + totally boundedness = compactness. Trying to prove.

Published on 29 Dec 2023 - 20:36

score 689 · Answer 3 · 2026-04-10 19:27:22

689

Views

The Existence of a Maximum Point for a Continuous Function on a Metric Space

Published on 10 Apr 2026 - 19:27

score 121 · Answer 4 · 2026-04-11 14:19:41

121

Views

Uniform Integrability and relative compactness

Published on 11 Apr 2026 - 14:19

score 49 · Answer 5 · 2026-04-10 23:31:10

49

Views

May a compactly supported real-valued function cross $0$ in its support finitely many times?

Published on 10 Apr 2026 - 23:31

score 73 · Answer 6 · 2026-04-02 16:19:28

73

Views

Let $X$ be the set of all Borel probability measures on [0,1] (include those Dirac Delta distributions), is $X$ locally compact Hausdorff?

Published on 02 Apr 2026 - 16:19

score 417 · Answer 7 · 2026-03-26 21:35:09

417

Views

One point (non-Hausdorff) compactification of compact space

Published on 26 Mar 2026 - 21:35

score 93 · Answer 8 · 2026-03-26 19:20:55

93

Views

Is the Alexandrov extension the unique $k_2$-Hausdorff one-point compactification of a KC space?

Published on 26 Mar 2026 - 19:20

score 118 · Answer 9 · 2026-03-26 16:18:02

118

Views

Fixed point property and compactness

Published on 26 Mar 2026 - 16:18

score 61 · Answer 10 · 2026-04-11 14:28:20

61

Views

Show that the image of S under the map $ f \mapsto f * g $ is a compact set in $ C_0([-2, 2])$.

Published on 11 Apr 2026 - 14:28

score 53 · Answer 11 · 2026-04-10 01:26:16

53

Views

Is the proof of "compact sets are closed" right?

Published on 10 Apr 2026 - 1:26

score 72 · Answer 12 · 2026-03-26 19:20:14

72

Views

Countably compact $T_0$ space $S$ such that for all $X\subseteq S$ and every $p\in X'$, there exists an open set $O$ such that ...

Published on 26 Mar 2026 - 19:20

score 84 · Answer 13 · 2026-04-08 21:48:57

84

Views

Is my set compact in $l^2$?

Published on 08 Apr 2026 - 21:48

score 30 · Answer 14 · 2026-03-25 22:23:34

30

Views

Orbit of closed set under compact group action

Published on 25 Mar 2026 - 22:23

score 41 · Answer 15 · 2024-01-10 12:19:02

41

Views

Can I choose $\varepsilon$ too small for there to be another element in $B(x,\varepsilon)$ in a normed space?

Published on 10 Jan 2024 - 12:19

List Question

Proving that $\mathbb{R}^ω$ is not $\sigma$-compact.

complete metric space + totally boundedness = compactness. Trying to prove.

The Existence of a Maximum Point for a Continuous Function on a Metric Space

Uniform Integrability and relative compactness

May a compactly supported real-valued function cross $0$ in its support finitely many times?

Let $X$ be the set of all Borel probability measures on [0,1] (include those Dirac Delta distributions), is $X$ locally compact Hausdorff?

One point (non-Hausdorff) compactification of compact space

Is the Alexandrov extension the unique $k_2$-Hausdorff one-point compactification of a KC space?

Fixed point property and compactness

Show that the image of S under the map $ f \mapsto f * g $ is a compact set in $ C_0([-2, 2])$.

Is the proof of "compact sets are closed" right?

Countably compact $T_0$ space $S$ such that for all $X\subseteq S$ and every $p\in X'$, there exists an open set $O$ such that ...

Is my set compact in $l^2$?

Orbit of closed set under compact group action

Can I choose $\varepsilon$ too small for there to be another element in $B(x,\varepsilon)$ in a normed space?

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