Countable powers of compact Abelian groups in the uniform topology and cardinality of their dual groups

We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X is the circle group: it is precisely 2^c.

Detalhes bibliográficos
Autores: Dikranjan, Dikran, Martín Peinador, Elena, Tarieladze, Vaja
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33450
Acesso em linha:https://hdl.handle.net/20.500.14352/33450
Access Level:acceso abierto
Palavra-chave:515.1
Character
dual group
uniform topology
connected group
precompact group
locally quasiconvex group.
Topología
1210 Topología
Descrição
Resumo:We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X is the circle group: it is precisely 2^c.