Question

Proving Matrix Lie Groups are Lie Groups without using Lie Algebras

score 84 · Answer 1 · 2026-03-27 02:50:39

84

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Proving Matrix Lie Groups are Lie Groups without using Lie Algebras

Published on 27 Mar 2026 - 2:50

score 61 · Answer 2 · 2022-07-30 16:23:29

61

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Show that if $(X,,\cal T)$ is a t. g. then $\text{cl}Y_1\text{cl}Y_2=\text{cl}(Y_1*Y_2)$ and $(\text{cl}Y)^{-1}=\text{cl}Y^{-1}$ where $Y_1,Y_2,Y⊆X$

Published on 30 Jul 2022 - 16:23

score 76 · Answer 3 · 2022-07-31 18:28:01

76

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If $Y$ is a subgroup of a topological group $(X,*,\cal T)$ then $Y$ is open if and only if $\operatorname{int}Y$ is not empty.

Published on 31 Jul 2022 - 18:28

score 125 · Answer 4 · 2026-03-26 09:41:14

125

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Maps from a profinite group to $\operatorname{GL}_n(\mathbb R)$.

Published on 26 Mar 2026 - 9:41

score 55 · Answer 5 · 2022-08-04 05:31:06

55

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Every discrete subgroup of a topological $T_1$ group is closed.

Published on 04 Aug 2022 - 5:31

score 225 · Answer 6 · 2026-03-29 18:31:41

225

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Prove that any topological group is completely regular.

Published on 29 Mar 2026 - 18:31

score 44 · Answer 7 · 2022-08-04 17:17:04

44

Views

Is this set of irreducible representations of a compact group finite?

Published on 04 Aug 2022 - 17:17

score 74 · Answer 8 · 2026-04-04 00:53:53

74

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Is there a topological group structure on the Baire Space?

Published on 04 Apr 2026 - 0:53

score 51 · Answer 9 · 2026-04-04 06:20:12

51

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Are all topological group structures on the Baire Space of the form $G^{\mathbb N}$ for $G$ a countable discrete group?

Published on 04 Apr 2026 - 6:20

score 33 · Answer 10 · 2026-02-23 10:07:18

33

Views

Is there an indecomposable topological group structure on the Baire Space?

Published on 23 Feb 2026 - 10:07

score 57 · Answer 11 · 2022-08-08 11:57:07

57

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If $H$ is a subgroup of $G$, then the homomorphism $i: HN/N \to p(H)$, defined by $i(xN) = p(x)$ is a topological isomorphism

Published on 08 Aug 2022 - 11:57

score 190 · Answer 12 · 2026-02-23 09:28:49

190

Views

Commutator subgroup of connected group.

Published on 23 Feb 2026 - 9:28

score 122 · Answer 13 · 2026-03-27 17:06:33

122

Views

Is assigning the central character a quotient map?

Published on 27 Mar 2026 - 17:06

score 54 · Answer 14 · 2026-03-29 16:00:49

54

Views

Showing the Krull topology is the same as the categorical limit topology of (infinite) Galois extensions - is my solution correct?

Published on 29 Mar 2026 - 16:00

score 193 · Answer 15 · 2026-03-26 09:40:06

193

Views

Possible holonomy groups of flat manifolds?

Published on 26 Mar 2026 - 9:40

List Question

Proving Matrix Lie Groups are Lie Groups without using Lie Algebras

Show that if $(X,,\cal T)$ is a t. g. then $\text{cl}Y_1\text{cl}Y_2=\text{cl}(Y_1*Y_2)$ and $(\text{cl}Y)^{-1}=\text{cl}Y^{-1}$ where $Y_1,Y_2,Y⊆X$

If $Y$ is a subgroup of a topological group $(X,*,\cal T)$ then $Y$ is open if and only if $\operatorname{int}Y$ is not empty.

Maps from a profinite group to $\operatorname{GL}_n(\mathbb R)$.

Every discrete subgroup of a topological $T_1$ group is closed.

Prove that any topological group is completely regular.

Is this set of irreducible representations of a compact group finite?

Is there a topological group structure on the Baire Space?

Are all topological group structures on the Baire Space of the form $G^{\mathbb N}$ for $G$ a countable discrete group?

Is there an indecomposable topological group structure on the Baire Space?

If $H$ is a subgroup of $G$, then the homomorphism $i: HN/N \to p(H)$, defined by $i(xN) = p(x)$ is a topological isomorphism

Commutator subgroup of connected group.

Is assigning the central character a quotient map?

Showing the Krull topology is the same as the categorical limit topology of (infinite) Galois extensions - is my solution correct?

Possible holonomy groups of flat manifolds?

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