Question

Separating Distributions with A Plane

score 80 · Answer 1 · 2026-04-15 08:05:12

80

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Separating Distributions with A Plane

Published on 15 Apr 2026 - 8:05

score 131 · Answer 2 · 2026-04-12 08:28:23

131

Views

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

Published on 12 Apr 2026 - 8:28

score 644 · Answer 3 · 2026-04-09 10:04:35

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 229 · Answer 4 · 2026-04-14 09:14:20

229

Views

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

Published on 14 Apr 2026 - 9:14

score 150 · Answer 5 · 2026-04-15 21:52:53

150

Views

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

Published on 15 Apr 2026 - 21:52

score 267 · Answer 6 · 2026-04-15 09:58:34

267

Views

Example of “almost metric” topological space

Published on 15 Apr 2026 - 9:58

score 862 · Answer 7 · 2026-05-03 11:20:53

862

Views

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

Published on 03 May 2026 - 11:20

score 147 · Answer 8 · 2026-05-10 15:47:58

147

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 10 May 2026 - 15:47

score 140 · Answer 9 · 2026-05-10 20:27:08

140

Views

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

Published on 10 May 2026 - 20:27

score 174 · Answer 10 · 2026-04-15 09:13:25

174

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 15 Apr 2026 - 9:13

score 99 · Answer 11 · 2026-04-17 11:37:34

99

Views

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

Published on 17 Apr 2026 - 11:37

score 80 · Answer 12 · 2026-04-13 17:44:00

80

Views

Seconed countable space is separable and first countable

Published on 13 Apr 2026 - 17:44

score 215 · Answer 13 · 2026-04-14 14:31:53

215

Views

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

Published on 14 Apr 2026 - 14:31

score 49 · Answer 14 · 2026-04-13 01:32:43

49

Views

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

Published on 13 Apr 2026 - 1:32

score 242 · Answer 15 · 2026-05-02 00:27:09

242

Views

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

Published on 02 May 2026 - 0:27

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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