List questions from topological-groups

Published on 26 Mar 2026 - 9:40

137

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Profinite groups are Galois groups

Published on 26 Mar 2026 - 11:16

282

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$GL_{n+1}(\mathbb R)/GL_n(\mathbb R)$ is not compact

Published on 14 Jan 2021 - 8:07

203

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When is Pontrjagin ring isomorphic to Cohomology ring (under coefficient $\Bbb{Z}_p$ and $\Bbb{Z}$)?

Published on 19 Jan 2021 - 11:26

113

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The Hausdorffness of a locally compact topological group

Published on 19 Jan 2021 - 16:18

232

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Topological groups: if $A$ is an open subset of $G$, then $A^{-1}$ is open.

Published on 21 Jan 2021 - 17:57

38

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Distinct topologies giving same topologies

Published on 26 Mar 2026 - 12:52

89

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An example of a compact abelian group that is not a torus

Published on 07 Feb 2021 - 17:08

103

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Image of a discrete group in a vector space is discrete and closed

Published on 09 Feb 2021 - 17:49

42

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Prove that $I_K/ \overline{K^*U}$ is totally disconnected.

Published on 25 Mar 2026 - 12:16

478

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Intuition behind Pontryagin duality

Published on 15 Feb 2021 - 21:59

43

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Trivialising homeomorphisms for a principal $G$-bundle as $G$-space morphisms

Published on 27 Mar 2026 - 23:13

51

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Whether Hausdorff Property is Required

Published on 28 Mar 2026 - 22:25

429

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the kernel of surjective homomorphism between topological groups is closed

Published on 03 Apr 2026 - 19:03

286

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Action of $\pi_1(G)$ on $\pi_n(G)$ is trivial for a topological group $G$, i.e. $G$ is a n-simple space.

Published on 25 Mar 2026 - 12:28

List Question

How to show that a Group is not profinite?

Profinite groups are Galois groups

$GL_{n+1}(\mathbb R)/GL_n(\mathbb R)$ is not compact

When is Pontrjagin ring isomorphic to Cohomology ring (under coefficient $\Bbb{Z}_p$ and $\Bbb{Z}$)?

The Hausdorffness of a locally compact topological group

Topological groups: if $A$ is an open subset of $G$, then $A^{-1}$ is open.

Distinct topologies giving same topologies

An example of a compact abelian group that is not a torus

Image of a discrete group in a vector space is discrete and closed

Prove that $I_K/ \overline{K^*U}$ is totally disconnected.

Intuition behind Pontryagin duality

Trivialising homeomorphisms for a principal $G$-bundle as $G$-space morphisms

Whether Hausdorff Property is Required

the kernel of surjective homomorphism between topological groups is closed

Action of $\pi_1(G)$ on $\pi_n(G)$ is trivial for a topological group $G$, i.e. $G$ is a n-simple space.

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