List questions from topological-groups

Published on 13 Apr 2016 - 16:33

504

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Let $G$ be a Lie group and $H$ be a closed subgroup of $G$. Show that if $H$ and homogeneous space $\frac{G}{H}$ are connected, then $G$ is connected.

Published on 26 Mar 2026 - 1:12

142

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Show that $ \operatorname{Sp}(n)=\{A \in M_n(\mathbb{H}) \mid AA^=I=A^A\} $ is a compact group

Published on 16 Apr 2016 - 16:29

969

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Closed subgroup implies open?

Published on 16 Apr 2016 - 22:30

698

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Lie group structures inside of Clifford algebras

Published on 27 Mar 2026 - 11:24

336

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$T_0$ is equivalent to $T_1$ in a topological group

Published on 27 Mar 2026 - 12:20

38

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If $f(gK) \subset U$ find a compact neighborhood of $g$, $\overline{Q}$, such that $f(\overline{Q} K) \subset U$

Published on 26 Mar 2026 - 14:22

62

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Euclidean Sphere

Published on 20 Apr 2016 - 8:30

54

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Sequences $(U_n)$ of neighborhoods of $0$ in a LCA group with $m(U_n)\to 0$

Published on 20 Apr 2016 - 15:29

629

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Fundamental groups of path connected subspaces

Published on 25 Apr 2016 - 2:45

226

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identity for quaternions' group Sp(n)=Sp(2n,C)∩U(2n)

Published on 28 Apr 2016 - 14:47

81

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Show that $S^1$ acts on $S^3$

Published on 02 May 2016 - 18:01

763

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Isomorphism theorems for topological groups

Published on 02 May 2016 - 21:12

84

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A dense set in $\mathbb{T}$

Published on 06 May 2016 - 0:26

36

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Showing some transformation is group isomorphism (topological group).

Published on 08 May 2016 - 20:12

List Question

Proving that $B:=\{f(x)\in C[a,b]:f(a)=0\}$ is close set

Let $G$ be a Lie group and $H$ be a closed subgroup of $G$. Show that if $H$ and homogeneous space $\frac{G}{H}$ are connected, then $G$ is connected.

Show that $ \operatorname{Sp}(n)=\{A \in M_n(\mathbb{H}) \mid AA^=I=A^A\} $ is a compact group

Closed subgroup implies open?

Lie group structures inside of Clifford algebras

$T_0$ is equivalent to $T_1$ in a topological group

If $f(gK) \subset U$ find a compact neighborhood of $g$, $\overline{Q}$, such that $f(\overline{Q} K) \subset U$

Euclidean Sphere

Sequences $(U_n)$ of neighborhoods of $0$ in a LCA group with $m(U_n)\to 0$

Fundamental groups of path connected subspaces

identity for quaternions' group Sp(n)=Sp(2n,C)∩U(2n)

Show that $S^1$ acts on $S^3$

Isomorphism theorems for topological groups

A dense set in $\mathbb{T}$

Showing some transformation is group isomorphism (topological group).

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