List questions from separable-spaces

Published on 04 Nov 2017 - 4:27

477

Views

Show that the Hilbert space $l^2$ equipped with the standard inner product and induced norm is separable (contains a countable, dense subset).

Published on 06 Nov 2017 - 15:35

64

Views

Existence of a countable orthonormal fundamental set in unitary separable spaces

Published on 09 Nov 2017 - 17:42

88

Views

$\langle f,g\rangle_H$ is $\mu$-mesurable

Published on 23 Nov 2017 - 18:14

665

Views

$\ell^\infty(\mathbb{N})$ is not separable

Published on 26 Nov 2017 - 10:55

705

Views

Show that $(C_b (0,1],||\cdot||_{\infty})$ is not separable

Published on 30 Nov 2017 - 23:13

232

Views

Finding a Schauder basis in a countable generating subset without Zorn's lemma

Published on 25 Mar 2026 - 20:35

155

Views

Separable spaces in topology

Published on 07 Dec 2017 - 8:45

176

Views

$X^$ with $w^$-topology second countable for separable Banach space $X$?

Published on 25 Mar 2026 - 20:09

1.3k

Views

How do you show that a Hilbert space is separable if and only if it has a countable dense subset?

Published on 06 Jan 2018 - 19:05

3k

Views

Proof of separability of $L^2(\mathbb{R})$ without Stone-Weierstrass Theorem

Published on 12 Jan 2018 - 19:22

263

Views

Compactification of separable metric spaces

Published on 12 Jan 2018 - 21:02

1.4k

Views

Sorgenfrey line is hereditarily separable

Published on 23 Feb 2026 - 8:36

1.5k

Views

Subspaces of Sorgenfrey line and a question about Lindelöf spaces

Published on 23 Feb 2026 - 8:41

12.7k

Views

Prove that $X^\ast$ separable implies $X$ separable

Published on 15 Nov 2011 - 15:09

List Question

Are the real numbers separable under the K-topology?

Show that the Hilbert space $l^2$ equipped with the standard inner product and induced norm is separable (contains a countable, dense subset).

Existence of a countable orthonormal fundamental set in unitary separable spaces

$\langle f,g\rangle_H$ is $\mu$-mesurable

$\ell^\infty(\mathbb{N})$ is not separable

Show that $(C_b (0,1],||\cdot||_{\infty})$ is not separable

Finding a Schauder basis in a countable generating subset without Zorn's lemma

Separable spaces in topology

$X^$ with $w^$-topology second countable for separable Banach space $X$?

How do you show that a Hilbert space is separable if and only if it has a countable dense subset?

Proof of separability of $L^2(\mathbb{R})$ without Stone-Weierstrass Theorem

Compactification of separable metric spaces

Sorgenfrey line is hereditarily separable

Subspaces of Sorgenfrey line and a question about Lindelöf spaces

Prove that $X^\ast$ separable implies $X$ separable

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