Question

An inner product space that every closed subspace is complemented, is it must be separable?

score 40 · Answer 1 · 2023-06-12 12:06:03

40

Views

An inner product space that every closed subspace is complemented, is it must be separable?

Published on 12 Jun 2023 - 12:06

score 17 · Answer 2 · 2023-06-18 06:26:36

17

Views

A question of countable product and uncountable product

Published on 18 Jun 2023 - 6:26

score 115 · Answer 3 · 2023-07-01 07:06:10

115

Views

Space of smooth differential forms with compact support on $U \subset \mathbb{R}^n$ is separable

Published on 01 Jul 2023 - 7:06

score 31 · Answer 4 · 2023-07-01 18:38:19

31

Views

Whether the function $(x,x')\mapsto\rho\big(f(x),f(x')\big)$ is Borel for a Borel map $f\colon (X,d)\to (Y,\rho)$ with $(Y,\rho)$ not being separable?

Published on 01 Jul 2023 - 18:38

score 28 · Answer 5 · 2026-03-25 12:50:10

28

Views

A particular covering made up by disjointed families of Closed Balls

Published on 25 Mar 2026 - 12:50

score 158 · Answer 6 · 2023-08-18 20:26:23

158

Views

Must a closed set with empty interior in a separable compact space of cardinality at most $2^{\aleph_{0}}$ be separable?

Published on 18 Aug 2023 - 20:26

score 133 · Answer 7 · 2023-08-24 03:20:07

133

Views

How to prove that $l^p$ is separable?

Published on 24 Aug 2023 - 3:20

score 88 · Answer 8 · 2023-10-10 19:59:20

88

Views

Difficulty interpreting and solving Baby Rudin Problem 2.25, and how to optimally progress through Baby Rudin?

Published on 10 Oct 2023 - 19:59

score 78 · Answer 9 · 2023-10-24 15:23:20

78

Views

$C(X, \mathbb{C})$ separable

Published on 24 Oct 2023 - 15:23

score 147 · Answer 10 · 2023-12-18 17:41:28

147

Views

Let $X$ be a normed space. Show that if $X^*$ is separable, then $X$ is separable and show that the reverse does not hold.

Published on 18 Dec 2023 - 17:41

score 55 · Answer 11 · 2026-02-23 10:22:30

55

Views

How to prove that an absolutely continuous function space on a finite closed interval is a separable space in this norm sense?

Published on 23 Feb 2026 - 10:22

score 99 · Answer 12 · 2024-01-06 03:44:59

99

Views

A separable Hilbert space has a countable orthonormal basis. Is this true also for Banach spaces?

Published on 06 Jan 2024 - 3:44

score 256 · Answer 13 · 2024-01-23 15:16:29

256

Views

Characterization of distance between points in separable space

Published on 23 Jan 2024 - 15:16

score 58 · Answer 14 · 2024-01-25 09:56:59

58

Views

Does a separable, $US$, sequential space have cardinality at most the continuum?

Published on 25 Jan 2024 - 9:56

score 48 · Answer 15 · 2026-02-23 04:55:10

48

Views

Locally compact Polish space admits a proper metric

Published on 23 Feb 2026 - 4:55

List Question

An inner product space that every closed subspace is complemented, is it must be separable?

A question of countable product and uncountable product

Space of smooth differential forms with compact support on $U \subset \mathbb{R}^n$ is separable

Whether the function $(x,x')\mapsto\rho\big(f(x),f(x')\big)$ is Borel for a Borel map $f\colon (X,d)\to (Y,\rho)$ with $(Y,\rho)$ not being separable?

A particular covering made up by disjointed families of Closed Balls

Must a closed set with empty interior in a separable compact space of cardinality at most $2^{\aleph_{0}}$ be separable?

How to prove that $l^p$ is separable?

Difficulty interpreting and solving Baby Rudin Problem 2.25, and how to optimally progress through Baby Rudin?

$C(X, \mathbb{C})$ separable

Let $X$ be a normed space. Show that if $X^*$ is separable, then $X$ is separable and show that the reverse does not hold.

How to prove that an absolutely continuous function space on a finite closed interval is a separable space in this norm sense?

A separable Hilbert space has a countable orthonormal basis. Is this true also for Banach spaces?

Characterization of distance between points in separable space

Does a separable, $US$, sequential space have cardinality at most the continuum?

Locally compact Polish space admits a proper metric

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