Question

If $X$ is separable then $X^∗$ is separable in all topologies $\tau$ such that $(X^∗,\tau)^∗ =X$?

score 42 · Answer 1 · 2020-05-28 19:00:09

42

Views

If $X$ is separable then $X^∗$ is separable in all topologies $\tau$ such that $(X^∗,\tau)^∗ =X$?

Published on 28 May 2020 - 19:00

score 80 · Answer 2 · 2020-06-02 14:00:02

80

Views

$X^*$ separable implies separable unit ball

Published on 02 Jun 2020 - 14:00

score 363 · Answer 3 · 2020-06-10 22:55:26

363

Views

Completion of a separable metric space is separable

Published on 10 Jun 2020 - 22:55

score 55 · Answer 4 · 2026-03-25 21:31:34

55

Views

If $d$ is a separable metric on a Banach space, approximate a $d$-Lipschitz function by Fréchet differentiable $d$-Lipschitz functions

Published on 25 Mar 2026 - 21:31

score 806 · Answer 5 · 2020-06-14 12:22:16

806

Views

Is there an alternative way to show that a finite dimensional vector space is separable?

Published on 14 Jun 2020 - 12:22

score 31 · Answer 6 · 2020-06-16 17:39:04

31

Views

a separable hilbert space and closed hyperplan

Published on 16 Jun 2020 - 17:39

score 56 · Answer 7 · 2020-06-30 14:21:05

56

Views

A metrizable TVS $E$ is separable, every noncountable subset of $E$ contains a convergent sequence.

Published on 30 Jun 2020 - 14:21

score 826 · Answer 8 · 2020-07-01 05:45:13

826

Views

Separable Hilbert space definition doubt

Published on 01 Jul 2020 - 5:45

score 104 · Answer 9 · 2020-07-06 11:45:56

104

Views

Continuously embedded subspace (with own topolog. structure) of a separable real Hilbert space is itself separable

Published on 06 Jul 2020 - 11:45

score 539 · Answer 10 · 2020-07-10 05:20:05

539

Views

Separability of $W^{1,p}(\Omega)$, when $1\leq p<\infty$

Published on 10 Jul 2020 - 5:20

score 185 · Answer 11 · 2020-07-19 04:35:47

185

Views

Using ${\rm Lip}1$ to show that $C[0,1]$ is separable

Published on 19 Jul 2020 - 4:35

score 162 · Answer 12 · 2020-07-24 07:30:45

162

Views

Example of Separable Product Space with cardinality greater than continuum?

Published on 24 Jul 2020 - 7:30

score 265 · Answer 13 · 2016-08-18 13:35:00

265

Views

Metric space as a countable union of $\epsilon$ sized sets

Published on 18 Aug 2016 - 13:35

score 282 · Answer 14 · 2026-03-25 11:10:46

282

Views

Constraining a dense sequence on a product space, one factor at a time

Published on 25 Mar 2026 - 11:10

score 143 · Answer 15 · 2026-03-25 14:00:34

143

Views

How can I prove 'separable' guarantees 'second countable'?

Published on 25 Mar 2026 - 14:00

List Question

If $X$ is separable then $X^∗$ is separable in all topologies $\tau$ such that $(X^∗,\tau)^∗ =X$?

$X^*$ separable implies separable unit ball

Completion of a separable metric space is separable

If $d$ is a separable metric on a Banach space, approximate a $d$-Lipschitz function by Fréchet differentiable $d$-Lipschitz functions

Is there an alternative way to show that a finite dimensional vector space is separable?

a separable hilbert space and closed hyperplan

A metrizable TVS $E$ is separable, every noncountable subset of $E$ contains a convergent sequence.

Separable Hilbert space definition doubt

Continuously embedded subspace (with own topolog. structure) of a separable real Hilbert space is itself separable

Separability of $W^{1,p}(\Omega)$, when $1\leq p<\infty$

Using ${\rm Lip}1$ to show that $C[0,1]$ is separable

Example of Separable Product Space with cardinality greater than continuum?

Metric space as a countable union of $\epsilon$ sized sets

Constraining a dense sequence on a product space, one factor at a time

How can I prove 'separable' guarantees 'second countable'?

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