Question

Is the space of continuous bounded real valued functions on a Polish space separable?

score 395 · Answer 1 · 2026-03-17 12:52:31

395

Views

Is the space of continuous bounded real valued functions on a Polish space separable?

Published on 17 Mar 2026 - 12:52

score 184 · Answer 2 · 2018-03-21 14:35:42

184

Views

Is a metric space separable if every proper subspace is separable?

Published on 21 Mar 2018 - 14:35

score 120 · Answer 3 · 2018-04-03 11:40:12

120

Views

A normed space is not separable when $\ell_\infty$ can be embedded isometrically into it

Published on 03 Apr 2018 - 11:40

score 536 · Answer 4 · 2026-03-25 06:09:58

536

Views

Separable dual implies space is weakly metrisable

Published on 25 Mar 2026 - 6:09

score 588 · Answer 5 · 2026-03-22 20:13:46

588

Views

Can a countable dense subset be split into two disjoint dense subsets?

Published on 22 Mar 2026 - 20:13

score 167 · Answer 6 · 2026-03-25 00:07:48

167

Views

Is the set of all the subsets of a completely separable space still completely separable?

Published on 25 Mar 2026 - 0:07

score 42 · Answer 7 · 2026-03-17 01:22:56

42

Views

Check properties of the topology $\{U \subseteq \mathbb{R} \mid \forall x \in U: \exists \epsilon > 0: [x, x + \epsilon[ \subseteq U\}$

Published on 17 Mar 2026 - 1:22

score 359 · Answer 8 · 2018-04-27 22:32:58

359

Views

Decreasing sequence of closed sets in a separable metric space

Published on 27 Apr 2018 - 22:32

score 491 · Answer 9 · 2018-05-10 12:05:23

491

Views

counting measure space is not separable but the corresponding $L^p$ space is separable

Published on 10 May 2018 - 12:05

score 434 · Answer 10 · 2018-05-13 09:59:32

434

Views

Intuition for the term "separable" in separable metric space

Published on 13 May 2018 - 9:59

score 3.1k · Answer 11 · 2018-05-19 15:52:33

3.1k

Views

Explicit Countable Orthonormal Basis for $L^2(\mathbb{R})$

Published on 19 May 2018 - 15:52

score 1.7k · Answer 12 · 2018-05-19 22:34:55

1.7k

Views

Show that if $X$ is locally compact and $\sigma$-compact then is separable

Published on 19 May 2018 - 22:34

score 655 · Answer 13 · 2026-03-22 02:31:56

655

Views

GNS construction and separability.

Published on 22 Mar 2026 - 2:31

score 78 · Answer 14 · 2026-03-22 15:56:13

78

Views

Separable topological spaces. Origin of terminology.

Published on 22 Mar 2026 - 15:56

score 380 · Answer 15 · 2026-03-22 07:12:58

380

Views

Is the dual to $C^1[0,1]$ separable?

Published on 22 Mar 2026 - 7:12

List Question

Is the space of continuous bounded real valued functions on a Polish space separable?

Is a metric space separable if every proper subspace is separable?

A normed space is not separable when $\ell_\infty$ can be embedded isometrically into it

Separable dual implies space is weakly metrisable

Can a countable dense subset be split into two disjoint dense subsets?

Is the set of all the subsets of a completely separable space still completely separable?

Check properties of the topology $\{U \subseteq \mathbb{R} \mid \forall x \in U: \exists \epsilon > 0: [x, x + \epsilon[ \subseteq U\}$

Decreasing sequence of closed sets in a separable metric space

counting measure space is not separable but the corresponding $L^p$ space is separable

Intuition for the term "separable" in separable metric space

Explicit Countable Orthonormal Basis for $L^2(\mathbb{R})$

Show that if $X$ is locally compact and $\sigma$-compact then is separable

GNS construction and separability.

Separable topological spaces. Origin of terminology.

Is the dual to $C^1[0,1]$ separable?

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