Question

If G is a separable metrizable group with at least two elements, then $G^{\omega_1}$ is a separable Fréchet group which is not metrizable.

score 59 · Answer 1 · 2016-11-04 00:33:18

If G is a separable metrizable group with at least two elements, then $G^{\omega_1}$ is a separable Fréchet group which is not metrizable.

score 146 · Answer 2 · 2016-11-11 22:50:04

146

Views

Calculus notation in Haar measure. What is really going on?

Published on 11 Nov 2016 - 22:50

score 78 · Answer 3 · 2016-11-12 04:47:31

78

Views

Why Does the Stabilizer of a Point Detect Singularities

Published on 12 Nov 2016 - 4:47

score 38 · Answer 4 · 2016-11-16 22:02:19

38

Views

(Complex number modulo Complex Number) $\mathbb{C} /n \mathbb{C}$

Published on 16 Nov 2016 - 22:02

score 577 · Answer 5 · 2016-11-17 11:53:14

577

Views

what is an open set in a topological group

Published on 17 Nov 2016 - 11:53

score 255 · Answer 6 · 2026-03-26 02:55:10

255

Views

Show that: - $\hat{\mathbb{Z}} \cong \mathbb{S^1}$ , $\hat{\mathbb{S^1}} \cong \mathbb{Z}$ , $\hat{\mathbb{R}} \cong \mathbb{R}$

Published on 26 Mar 2026 - 2:55

score 441 · Answer 7 · 2016-11-23 04:04:40

441

Views

Dense subset of Compact Topological Group

Published on 23 Nov 2016 - 4:04

score 100 · Answer 8 · 2016-11-23 10:36:53

100

Views

Show that $\hat{G_1} \times \hat{G_2} \cong \widehat {G_1 \times G_2}$

Published on 23 Nov 2016 - 10:36

score 44 · Answer 9 · 2026-03-26 02:55:48

44

Views

Show that either $\mu(S) = 0$ or $\mu(G \setminus S) = 0$

Published on 26 Mar 2026 - 2:55

score 35 · Answer 10 · 2026-03-26 04:38:05

35

Views

Can all connected locally compact groups be written as a product of abelian and compact subgroups?

Published on 26 Mar 2026 - 4:38

score 50 · Answer 11 · 2026-03-26 04:38:11

50

Views

Prove $G = \{ a + b \hat{i} +c \hat{j} +d \hat{k} : a,b,c,d \in \mathbb{R} \}$ is a locally compact topological group

Published on 26 Mar 2026 - 4:38

score 98 · Answer 12 · 2016-11-24 05:03:45

98

Views

Whitehead's problem equivalent.

Published on 24 Nov 2016 - 5:03

score 75 · Answer 13 · 2016-11-28 09:15:07

75

Views

Subgroup of intersection of clopen sets gets smaller and smaller

Published on 28 Nov 2016 - 9:15

score 312 · Answer 14 · 2026-03-25 11:08:02

312

Views

Some question about first (or second) countable - first (second) "countabilization"

Published on 25 Mar 2026 - 11:08

score 157 · Answer 15 · 2026-03-26 17:37:32

157

Views

Is there a nontrivial left-invariant Borel measure (necessarily not Radon) that is not a constant multiple of Haar?

Published on 26 Mar 2026 - 17:37

List Question

If G is a separable metrizable group with at least two elements, then $G^{\omega_1}$ is a separable Fréchet group which is not metrizable.

Calculus notation in Haar measure. What is really going on?

Why Does the Stabilizer of a Point Detect Singularities

(Complex number modulo Complex Number) $\mathbb{C} /n \mathbb{C}$

what is an open set in a topological group

Show that: - $\hat{\mathbb{Z}} \cong \mathbb{S^1}$ , $\hat{\mathbb{S^1}} \cong \mathbb{Z}$ , $\hat{\mathbb{R}} \cong \mathbb{R}$

Dense subset of Compact Topological Group

Show that $\hat{G_1} \times \hat{G_2} \cong \widehat {G_1 \times G_2}$

Show that either $\mu(S) = 0$ or $\mu(G \setminus S) = 0$

Can all connected locally compact groups be written as a product of abelian and compact subgroups?

Prove $G = \{ a + b \hat{i} +c \hat{j} +d \hat{k} : a,b,c,d \in \mathbb{R} \}$ is a locally compact topological group

Whitehead's problem equivalent.

Subgroup of intersection of clopen sets gets smaller and smaller

Some question about first (or second) countable - first (second) "countabilization"

Is there a nontrivial left-invariant Borel measure (necessarily not Radon) that is not a constant multiple of Haar?

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