Question

Separable topological space where the dense subset remains dense after deleting finitely many points

score 53 · Answer 1 · 2022-02-05 14:29:43

53

Views

Separable topological space where the dense subset remains dense after deleting finitely many points

Published on 05 Feb 2022 - 14:29

score 87 · Answer 2 · 2026-02-23 08:37:55

87

Views

Baire space which doesn't contain a dense completely metrizable subspace

Published on 23 Feb 2026 - 8:37

score 108 · Answer 3 · 2022-02-12 08:55:19

108

Views

The idea behind the proof that if $E'$ is separable, then so is $E$

Published on 12 Feb 2022 - 8:55

score 121 · Answer 4 · 2022-02-13 15:08:17

121

Views

The normed space of convergent sequences of real numbers is separable (proof verification)

Published on 13 Feb 2022 - 15:08

score 54 · Answer 5 · 2022-02-14 21:19:24

54

Views

Any nonempty irreflexive Banach space contains a separable irreflexive Banach subspace - is my proof correct?

Published on 14 Feb 2022 - 21:19

score 328 · Answer 6 · 2022-02-15 17:48:44

328

Views

$L^p(\Omega)$ is separable for $1 \leq p <\infty$

Published on 15 Feb 2022 - 17:48

score 44 · Answer 7 · 2022-02-16 20:04:57

44

Views

If $O_a=\{f \in L^\infty(\Omega):\|f-u_a\|_\infty<\frac{1}{2}\}$ then $O_a \cap O_b=\emptyset$ if $a \neq b$

Published on 16 Feb 2022 - 20:04

score 62 · Answer 8 · 2026-02-23 23:08:04

62

Views

Is there a nontrivial but short example where the separable degree is strictly less than the degree of a field extension?

Published on 23 Feb 2026 - 23:08

score 30 · Answer 9 · 2022-02-27 14:25:07

30

Views

Inequivalence metrics generate same Borel $\sigma$-field.

Published on 27 Feb 2022 - 14:25

score 47 · Answer 10 · 2022-03-03 16:05:39

47

Views

There is an isometry from a separable normed space $E$ into $\ell^\infty$

Published on 03 Mar 2022 - 16:05

score 364 · Answer 11 · 2026-02-23 11:50:20

364

Views

Brezis's Ex 3.22: If $E$ is reflexive, there is a sequence of norm $1$ that weakly converges to $0$

Published on 23 Feb 2026 - 11:50

score 237 · Answer 12 · 2026-02-23 08:39:37

237

Views

Prob. 5 (a), Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Every metrizabe separable space is second-countable

Published on 23 Feb 2026 - 8:39

score 178 · Answer 13 · 2022-03-05 22:46:15

178

Views

Is this a typo in Brezis's Ex 3.24?

Published on 05 Mar 2022 - 22:46

score 156 · Answer 14 · 2022-03-08 15:36:59

156

Views

Is the dual of a strictly convex Banach space strictly convex?

Published on 08 Mar 2022 - 15:36

score 121 · Answer 15 · 2022-03-14 07:38:40

121

Views

Construct an equivalent and strictly convex norm on a separable Banach space whose dual norm is also strictly convex

Published on 14 Mar 2022 - 7:38

List Question

Separable topological space where the dense subset remains dense after deleting finitely many points

Baire space which doesn't contain a dense completely metrizable subspace

The idea behind the proof that if $E'$ is separable, then so is $E$

The normed space of convergent sequences of real numbers is separable (proof verification)

Any nonempty irreflexive Banach space contains a separable irreflexive Banach subspace - is my proof correct?

$L^p(\Omega)$ is separable for $1 \leq p <\infty$

If $O_a=\{f \in L^\infty(\Omega):\|f-u_a\|_\infty<\frac{1}{2}\}$ then $O_a \cap O_b=\emptyset$ if $a \neq b$

Is there a nontrivial but short example where the separable degree is strictly less than the degree of a field extension?

Inequivalence metrics generate same Borel $\sigma$-field.

There is an isometry from a separable normed space $E$ into $\ell^\infty$

Brezis's Ex 3.22: If $E$ is reflexive, there is a sequence of norm $1$ that weakly converges to $0$

Prob. 5 (a), Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Every metrizabe separable space is second-countable

Is this a typo in Brezis's Ex 3.24?

Is the dual of a strictly convex Banach space strictly convex?

Construct an equivalent and strictly convex norm on a separable Banach space whose dual norm is also strictly convex

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