Duality of topological groups (Q1821883)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Duality of topological groups |
scientific article; zbMATH DE number 4000245
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Duality of topological groups |
scientific article; zbMATH DE number 4000245 |
Statements
Duality of topological groups (English)
0 references
1985
0 references
A topological group \(G^*\) is called a dual to a topological group G if there exists a duality isomorphism between the lattices of all closed subgroups, L(G) and \(L(G^*)\). Let G be a locally compact group with nontrivial connected component \(G_ 0\) and with compact factorgroup \(G/G_ 0\). If G has a dual group then G is abelian. This is the main result of the paper. The author also describes profinite groups with duals.
0 references
lattices of closed subgroups
0 references
topological group
0 references
duality isomorphism
0 references
locally compact group
0 references
dual group
0 references
profinite groups
0 references
