topological group
C18167
concept
A topological group is a group equipped with a topology such that the group operation and inversion are continuous maps with respect to that topology.
All labels observed (14)
| Label | Occurrences |
|---|---|
| topological group canonical | 13 |
| connected Lie group | 7 |
| discrete group | 5 |
| compact Lie group | 4 |
| Fuchsian group | 2 |
| Lie group action | 1 |
| arithmetic group | 1 |
| concept in topological group theory | 1 |
| locally compact group | 1 |
| matrix Lie group | 1 |
| p-adic Lie group | 1 |
| simply connected Lie group | 1 |
| topological group theory concept | 1 |
| universal covering group | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: topological group
Generated description
A topological group is a group equipped with a topology such that the group operation and inversion are continuous maps with respect to that topology.
Instances (30)
| Instance | Via concept surface |
|---|---|
| Euclidean group | — |
| E(n) | — |
| Lie group | — |
|
PSL(2,ℤ)
linked to:
modular group PSL(2,Z)
|
discrete group |
|
SO(3)
linked to:
rotation group SO(3)
|
— |
| SL(2,C) | connected Lie group |
| SU(3) | matrix Lie group |
| Weil group | — |
| Kleinian group | discrete group |
| (2,3,7) triangle group | Fuchsian group |
|
SU(2)
linked to:
rotation group SU(2)
|
compact Lie group |
| Fuchsian group | discrete group |
| ISO(n) | — |
|
SO(n)
linked to:
special orthogonal group SO(n)
|
— |
| U(1) | — |
| p-adic analytic groups | topological group theory concept |
| Spin(2,d) | universal covering group |
|
SU(n)
linked to:
special unitary group SU(n)
|
compact Lie group |
|
GL(n,ℝ)
linked to:
general linear group GL(n,R)
|
— |
|
GL(n,ℂ)
linked to:
general linear group GL(n,C)
|
— |
|
SL(n,ℂ)
linked to:
special linear group SL(n,C)
|
connected Lie group |
| SL(2,ℤ) | discrete group |
| PSL(2,ℝ) | connected Lie group |
| Pauli group | discrete group |
| SL(2,R) | connected Lie group |
| Haar measure | concept in topological group theory |
| Weil–Deligne group | — |
| idèle class group | — |
| metaplectic group | — |
|
PSL(2,ℂ)
linked to:
PSL(2,\mathbb{C})
|
connected Lie group |