Question

Separating Distributions with A Plane

score 77 · Answer 1 · 2020-04-21 18:21:14

77

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Separating Distributions with A Plane

Published on 21 Apr 2020 - 18:21

score 130 · Answer 2 · 2026-02-24 05:36:19

130

Views

Prove the compactness and second countability of a subset of $\Bbb{R}^{L^1(G)\times D}$

Published on 24 Feb 2026 - 5:36

score 643 · Answer 3 · 2026-02-23 06:25:52

Show that if the norms ∥⋅∥1 and ∥⋅∥2 are equivalent, then if space (X,∥⋅∥1) is complete, then the space (X,∥⋅∥2) is not necessary complete.

score 226 · Answer 4 · 2020-04-30 16:55:41

226

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Prob. 10, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: A countable product of separable spaces is also separable

Published on 30 Apr 2020 - 16:55

score 147 · Answer 5 · 2020-04-30 18:33:03

147

Views

Prob. 13, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Every collection of disjoint open sets in a separable space is countable

Published on 30 Apr 2020 - 18:33

score 264 · Answer 6 · 2020-04-30 19:39:32

264

Views

Example of “almost metric” topological space

Published on 30 Apr 2020 - 19:39

score 859 · Answer 7 · 2026-02-23 03:20:39

859

Views

Prob. 11, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: A continuous image of a Lindelof (separable) space is Lindelof (separable)

Published on 23 Feb 2026 - 3:20

score 146 · Answer 8 · 2026-03-25 12:28:07

146

Views

Prob. 15, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: The subspace $\mathscr{C}(I,\mathbb{R})$ of $\mathbb{R}^I$ with uniform metric is separable

Published on 25 Mar 2026 - 12:28

score 137 · Answer 9 · 2026-03-25 13:56:22

137

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Prob. 16 (a), Sec. 30, in Munkres' TOPOLOGY, 2nd ed: The product space $\mathbb{R}^I$, where $I = [0, 1]$, is separable

Published on 25 Mar 2026 - 13:56

score 171 · Answer 10 · 2020-05-14 19:41:18

171

Views

If $X$ is separable, $Y$ is $T_2$ and $f: X \to Y$ is continuous, then $f$ is decided by the values of a countable dense set

Published on 14 May 2020 - 19:41

score 94 · Answer 11 · 2020-05-16 11:14:23

94

Views

Is my proof of the separability of the closure of the range of a compact operator correct?

Published on 16 May 2020 - 11:14

score 77 · Answer 12 · 2020-05-17 18:48:58

77

Views

Seconed countable space is separable and first countable

Published on 17 May 2020 - 18:48

score 212 · Answer 13 · 2020-05-19 00:44:36

212

Views

The space of bounded linear map from $L^2(\mathbb{R})$ to $L^2(\mathbb{R})$ is not separable.

Published on 19 May 2020 - 0:44

score 46 · Answer 14 · 2020-05-19 22:19:20

46

Views

Separability of a space implies existence of an element with positive measure neighborhood.

Published on 19 May 2020 - 22:19

score 237 · Answer 15 · 2026-02-23 02:56:24

237

Views

Show that if $X$ is compact metrizable then $C(X)$ is separable.

Published on 23 Feb 2026 - 2:56

List Question

Separating Distributions with A Plane

Prove the compactness and second countability of a subset of $\Bbb{R}^{L^1(G)\times D}$

Show that if the norms ∥⋅∥1 and ∥⋅∥2 are equivalent, then if space (X,∥⋅∥1) is complete, then the space (X,∥⋅∥2) is not necessary complete.

Prob. 10, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: A countable product of separable spaces is also separable

Prob. 13, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Every collection of disjoint open sets in a separable space is countable

Example of “almost metric” topological space

Prob. 11, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: A continuous image of a Lindelof (separable) space is Lindelof (separable)

Prob. 15, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: The subspace $\mathscr{C}(I,\mathbb{R})$ of $\mathbb{R}^I$ with uniform metric is separable

Prob. 16 (a), Sec. 30, in Munkres' TOPOLOGY, 2nd ed: The product space $\mathbb{R}^I$, where $I = [0, 1]$, is separable

If $X$ is separable, $Y$ is $T_2$ and $f: X \to Y$ is continuous, then $f$ is decided by the values of a countable dense set

Is my proof of the separability of the closure of the range of a compact operator correct?

Seconed countable space is separable and first countable

The space of bounded linear map from $L^2(\mathbb{R})$ to $L^2(\mathbb{R})$ is not separable.

Separability of a space implies existence of an element with positive measure neighborhood.

Show that if $X$ is compact metrizable then $C(X)$ is separable.

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