List questions from separable-spaces

Published on 25 Mar 2026 - 14:18

27.3k

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Prove if $X$ is a compact metric space, then $X$ is separable.

Published on 15 Oct 2014 - 0:58

960

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A metric that makes $l^\infty$ separable

Published on 01 Dec 2014 - 4:19

486

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$X$ compact metric implies $X$ separable

Published on 01 Dec 2014 - 16:53

897

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When is $L^2(\mu)$ separable?

Published on 04 Oct 2019 - 18:11

820

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Is separability a topological property?

Published on 09 Oct 2019 - 18:00

489

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Example for $\mathbb{X}/\mathbb{M}$ separable but $\mathbb{X}$ is not.

Published on 19 Oct 2019 - 17:44

1.2k

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Is $\mathbb{Q}^n$ countable?

Published on 25 Mar 2026 - 8:02

98

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When is $(L^\infty (\mathbb{R}, \mu); \|\cdot\|_{L^\infty (\mathbb{R}, \mu)})$ separable?

Published on 06 Nov 2019 - 22:56

343

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$C_0(X)$ is separable if $X$ is locally compact $\sigma$-compact metric space

Published on 15 Nov 2019 - 8:05

315

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Measurability of distance function

Published on 15 Nov 2019 - 11:32

45

Views

Slightly weaker notion of total boundedness and separability

Published on 15 Nov 2019 - 19:54

300

Views

Proof verification: Every separable metrizable space is second-countable.

Published on 25 Mar 2026 - 9:22

281

Views

Is every closed set a set of limit points of a sequence?

Published on 27 Nov 2019 - 10:16

83

Views

Is the space $(\mathbb{R}\setminus\mathbb{Q},d)$ separable with the metric $d(x,y)=\frac{|x-y|}{1+|x-y|}$?

Published on 09 Dec 2019 - 20:14

List Question

Separable implies second countable

Prove if $X$ is a compact metric space, then $X$ is separable.

A metric that makes $l^\infty$ separable

$X$ compact metric implies $X$ separable

When is $L^2(\mu)$ separable?

Is separability a topological property?

Example for $\mathbb{X}/\mathbb{M}$ separable but $\mathbb{X}$ is not.

Is $\mathbb{Q}^n$ countable?

When is $(L^\infty (\mathbb{R}, \mu); \|\cdot\|_{L^\infty (\mathbb{R}, \mu)})$ separable?

$C_0(X)$ is separable if $X$ is locally compact $\sigma$-compact metric space

Measurability of distance function

Slightly weaker notion of total boundedness and separability

Proof verification: Every separable metrizable space is second-countable.

Is every closed set a set of limit points of a sequence?

Is the space $(\mathbb{R}\setminus\mathbb{Q},d)$ separable with the metric $d(x,y)=\frac{|x-y|}{1+|x-y|}$?

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