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Pontryagin duality in the class of precompact Abelian groups and the Baire property

Autor
Bruguera, M.; Tkachenko, M.
Tipus d'activitat
Article en revista
Revista
Journal of pure and applied algebra
Data de publicació
2012
Volum
216
Número
12
Pàgina inicial
2636
Pàgina final
2647
Repositori
http://hdl.handle.net/2117/16724 Obrir en finestra nova
URL
http://arxiv.org/pdf/1101.4504v1.pdf Obrir en finestra nova
Resum
We present a wide class of reflexive, precompact, non-compact, Abelian topological groups G determined by three requirements. They must have the Baire property, satisfy the open refinement condition, and contain no infinite compact subsets. This combination of properties guarantees that all compact subsets of the dual group G∧ are finite. We also show that many (non-reflexive) precompact Abelian groups are quotients of reflexive precompact Abelian groups. This includes all precompact almost me...
Citació
Bruguera, M.; Tkachenko, M. Pontryagin duality in the class of precompact Abelian groups and the Baire property. "Journal of pure and applied algebra", 2012, vol. 216, núm. 12, p. 2636-2647.
Paraules clau
Almost metrizable, Baire property, Convergent sequence, Open refinement condition, Precompact, Pseudocompact, Reflexive, h-embedded subgroup
Grup de recerca
EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions

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