Pontryagin duality in the class of precompact Abelian groups and the Baire property
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...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/16724 |
| Acceso en línea: | https://hdl.handle.net/2117/16724 |
| Access Level: | acceso abierto |
| Palabra clave: | Harmonic analysis Topological groups Reflexive Precompact Pseudocompact Baire property Open refinement condition h-embedded subgroup Convergent sequence Almost metrizable Anàlisi harmònica Grups topològics Classificació AMS::43 Abstract harmonic analysis Classificació AMS::22 Topological groups, lie groups::22D Locally compact groups and their algebras Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia |
| Sumario: | 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 metrizable groups with the Baire property and their products. Finally, given a compact Abelian group G of weight ≥ 2!, we find proper dense subgroups H1 and H2 of G such that H1 is reflexive and pseudocompact, while H2 is non-reflexive and almost metrizable. |
|---|