Question

For a discrete topological space $X$, is Perm$(X)$ a topological group as a subspace of product topological space $X^X$?

score 185 · Answer 1 · 2026-05-03 00:23:26

185

Views

For a discrete topological space $X$, is Perm$(X)$ a topological group as a subspace of product topological space $X^X$?

Published on 03 May 2026 - 0:23

score 71 · Answer 2 · 2026-04-15 15:46:20

71

Views

Open subgroup of $\mathrm{Aut}(M) \subseteq M^M$ where $M$ is an $L$-structure for a first order language $L$ and $M$ has discrete topology

Published on 15 Apr 2026 - 15:46

score 97 · Answer 3 · 2026-04-15 23:39:35

97

Views

Is there a specific name for non-homotopic loops encircling same point?

Published on 15 Apr 2026 - 23:39

score 201 · Answer 4 · 2026-04-15 09:11:47

201

Views

If the product topology is connected, then the original topology is connected

Published on 15 Apr 2026 - 9:11

score 205 · Answer 5 · 2026-04-29 12:09:36

205

Views

Is there active research on topological groups?

Published on 29 Apr 2026 - 12:09

score 77 · Answer 6 · 2026-04-23 17:35:32

77

Views

Torsion in weird groups

Published on 23 Apr 2026 - 17:35

score 440 · Answer 7 · 2026-04-14 09:06:10

440

Views

On which topological spaces, can we give a group structure to make it a topological group?

Published on 14 Apr 2026 - 9:06

score 31 · Answer 8 · 2026-04-15 08:43:42

31

Views

The relation between two representations whose restrictions to a subgroup are the same

Published on 15 Apr 2026 - 8:43

score 158 · Answer 9 · 2026-04-14 06:29:41

158

Views

Infinite Galois theory and $ \mathbb{N}^{ \mathbb{N}} $.

Published on 14 Apr 2026 - 6:29

score 199 · Answer 10 · 2026-04-12 12:19:00

199

Views

Pontryagin Self-Duality

Published on 12 Apr 2026 - 12:19

score 73 · Answer 11 · 2026-04-14 20:04:55

73

Views

Analogue of $O(n) \subset GL(n,\mathbb{R})$ in $Diff, PL, TOP$

Published on 14 Apr 2026 - 20:04

score 45 · Answer 12 · 2026-04-16 11:49:05

If $G$ is a paratopological group, is true that if $K$ is a compact subset of $G$ and $F$ is a closed subset of $G$ then $KF$ is closed in $G$?

score 304 · Answer 13 · 2026-04-15 22:22:06

304

Views

A Lie Group and Lie Algebra Problem

Published on 15 Apr 2026 - 22:22

score 44 · Answer 14 · 2026-04-19 18:00:11

44

Views

$\{g\in G: gU=V\}$ in a Polish group

Published on 19 Apr 2026 - 18:00

score 46 · Answer 15 · 2026-05-02 10:15:16

46

Views

$\iota\left(\mathbb Q\right)\subset\mathbb A_\mathbb Q$ is a lattice (diagonal embedding).

Published on 02 May 2026 - 10:15

List Question

For a discrete topological space $X$, is Perm$(X)$ a topological group as a subspace of product topological space $X^X$?

Open subgroup of $\mathrm{Aut}(M) \subseteq M^M$ where $M$ is an $L$-structure for a first order language $L$ and $M$ has discrete topology

Is there a specific name for non-homotopic loops encircling same point?

If the product topology is connected, then the original topology is connected

Is there active research on topological groups?

Torsion in weird groups

On which topological spaces, can we give a group structure to make it a topological group?

The relation between two representations whose restrictions to a subgroup are the same

Infinite Galois theory and $ \mathbb{N}^{ \mathbb{N}} $.

Pontryagin Self-Duality

Analogue of $O(n) \subset GL(n,\mathbb{R})$ in $Diff, PL, TOP$

If $G$ is a paratopological group, is true that if $K$ is a compact subset of $G$ and $F$ is a closed subset of $G$ then $KF$ is closed in $G$?

A Lie Group and Lie Algebra Problem

$\{g\in G: gU=V\}$ in a Polish group

$\iota\left(\mathbb Q\right)\subset\mathbb A_\mathbb Q$ is a lattice (diagonal embedding).

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