Question

$X^$ with $weak^$-topology is first category in itself when $X$ is infinite dimensional Fréchet space

score 365 · Answer 1 · 2026-04-16 14:59:55

365

Views

$X^$ with $weak^$-topology is first category in itself when $X$ is infinite dimensional Fréchet space

Published on 16 Apr 2026 - 14:59

score 779 · Answer 2 · 2026-04-13 00:43:08

779

Views

$L^1([0,1])$ closed unit ball is not weakly compact

Published on 13 Apr 2026 - 0:43

score 89 · Answer 3 · 2026-04-15 05:00:04

89

Views

Weak closure of subsets of the unitary sphere of a Banach space.

Published on 15 Apr 2026 - 5:00

score 77 · Answer 4 · 2026-04-11 08:37:13

77

Views

Rudin functional analysis, section 3.8 (Topological preliminaries)

Published on 11 Apr 2026 - 8:37

score 314 · Answer 5 · 2026-04-15 05:35:14

314

Views

Prove the mapping $(x,y)\mapsto x+y$ from $X \times X \to X$ is continuous when $X$ is given a weak topology.

Published on 15 Apr 2026 - 5:35

score 68 · Answer 6 · 2026-04-12 02:45:05

68

Views

A set $C$ that is not closed in the weak* topology

Published on 12 Apr 2026 - 2:45

score 1.9k · Answer 7 · 2026-04-09 00:42:02

1.9k

Views

Why are weak topologies useful in functional analysis?

Published on 09 Apr 2026 - 0:42

score 301 · Answer 8 · 2026-04-16 21:10:11

301

Views

Rudin's functional analysis theorem 3.10, proof that multiplication is continuous

Published on 16 Apr 2026 - 21:10

score 168 · Answer 9 · 2026-04-13 22:43:00

168

Views

Rudin's functional analysis theorem 3.12

Published on 13 Apr 2026 - 22:43

score 128 · Answer 10 · 2026-04-14 02:18:21

128

Views

The image of the weak topology with the canonical injection $J$

Published on 14 Apr 2026 - 2:18

score 56 · Answer 11 · 2026-04-13 16:57:58

56

Views

Is a metrizable and compact subset of $E^$ is a metrizable complete subset ? for the weak topology

Published on 13 Apr 2026 - 16:57

score 201 · Answer 12 · 2026-04-09 23:32:32

201

Views

Proof theorem 3.17 Rudin's functional analysis

Published on 09 Apr 2026 - 23:32

score 28 · Answer 13 · 2026-04-15 09:00:31

28

Views

Relation between energy functionals of stationary and dynamic version of a PDE.

Published on 15 Apr 2026 - 9:00

score 155 · Answer 14 · 2026-04-14 15:37:38

155

Views

Compactness in weak$^*$-topology on $l_1(\mathbb{N})$

Published on 14 Apr 2026 - 15:37

score 1.7k · Answer 15 · 2026-04-15 22:25:01

1.7k

Views

A weakly convergent sequence in a compact set, is strongly convegnet

Published on 15 Apr 2026 - 22:25

List Question

$X^$ with $weak^$-topology is first category in itself when $X$ is infinite dimensional Fréchet space

$L^1([0,1])$ closed unit ball is not weakly compact

Weak closure of subsets of the unitary sphere of a Banach space.

Rudin functional analysis, section 3.8 (Topological preliminaries)

Prove the mapping $(x,y)\mapsto x+y$ from $X \times X \to X$ is continuous when $X$ is given a weak topology.

A set $C$ that is not closed in the weak* topology

Why are weak topologies useful in functional analysis?

Rudin's functional analysis theorem 3.10, proof that multiplication is continuous

Rudin's functional analysis theorem 3.12

The image of the weak topology with the canonical injection $J$

Is a metrizable and compact subset of $E^$ is a metrizable complete subset ? for the weak topology

Proof theorem 3.17 Rudin's functional analysis

Relation between energy functionals of stationary and dynamic version of a PDE.

Compactness in weak$^*$-topology on $l_1(\mathbb{N})$

A weakly convergent sequence in a compact set, is strongly convegnet

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