Topological groups, Lie groups Topological groups: basic notions Concept
Open subgroup
Summary
An open subgroup of a topological group is a subgroup that is an open set. Open subgroups are also closed, so they are unions of connected components. They are central in the study of totally disconnected groups. In a profinite group the open normal subgroups form a base of neighbourhoods of the identity. A connected topological group has no open subgroup other than itself.
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| Tag | QYCFH68RD1 |
|---|---|
| URI | m2://QYCFH68RD1 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 22A05 |
| Specializes | Subgroup |
| Changed | 2 November 2026 |
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Used by
- Pro-p group
- van Dantzig's theorem
- Cayley–Abels graph
- Hecke algebra of a locally compact group
- Open subgroups are closed
- Lazard's theorem on p-adic analytic groups
- Gleason–Yamabe theorem