List questions from separable-spaces

Published on 25 Mar 2026 - 17:23

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Properties of Infinite set on co-finite topology and Countable set on co-countable topology

Published on 15 Jun 2016 - 5:03

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Every separable metric space has cardinality less than or equal to the cardinality of the continuum.

Published on 29 Jun 2016 - 13:09

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$X$ second countable locally compact Hausdorff implies $C(X)$ separable?

Published on 25 Mar 2026 - 18:52

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separability of a space

Published on 14 Jun 2013 - 12:52

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the product space $\mathbb{R}^I$,where I denote $[0,1]$, has a countable dense subset.

Published on 14 Jun 2013 - 16:12

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Prove the image of separable space under continuous function is separable.

Published on 21 Jun 2013 - 6:47

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A metric space is separable iff it is second countable

Published on 25 Mar 2026 - 18:52

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Show that $C(X,\Bbb R)$ is not separable

Published on 16 Aug 2013 - 10:34

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Prove that sequence space $\ell_p(\mathbb R)$ is separable

Published on 08 Sep 2013 - 12:21

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Prove that the space has a countable dense subset

Published on 09 Sep 2013 - 17:27

1.3k

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Separability of the finite complement topology on the real line.

Published on 22 Sep 2013 - 1:04

2.4k

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Every subspace of $\mathbb{R}$ with the lower limit topology is separable

Published on 23 Feb 2026 - 6:38

2.8k

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Uncountable product of separable spaces is separable?

Published on 14 Oct 2013 - 23:36

32.6k

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Why is $l^\infty$ not separable?

Published on 02 Feb 2014 - 7:17

List Question

Every separable metric space has a countable base

Properties of Infinite set on co-finite topology and Countable set on co-countable topology

Every separable metric space has cardinality less than or equal to the cardinality of the continuum.

$X$ second countable locally compact Hausdorff implies $C(X)$ separable?

separability of a space

the product space $\mathbb{R}^I$,where I denote $[0,1]$, has a countable dense subset.

Prove the image of separable space under continuous function is separable.

A metric space is separable iff it is second countable

Show that $C(X,\Bbb R)$ is not separable

Prove that sequence space $\ell_p(\mathbb R)$ is separable

Prove that the space has a countable dense subset

Separability of the finite complement topology on the real line.

Every subspace of $\mathbb{R}$ with the lower limit topology is separable

Uncountable product of separable spaces is separable?

Why is $l^\infty$ not separable?

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