Completeness properties of locally quasi-convex groups
It is natural to extend the Grothendieck Theorem on completeness, valid for locally convex topological vector spaces, to abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, in this paper we present examples of metrizable locally...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1999 |
| 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:2117/760 |
| Acceso en línea: | https://hdl.handle.net/2117/760 |
| Access Level: | acceso abierto |
| Palabra clave: | Topological groups Topological linear spaces Topology Completeness Pontryagin duality theorem dual group Grothendieck theorem convergence group continuous convergence reflexive group k-space k-group Grups topològics Lie, Grups de Espais topològics Topologia Classificació AMS::22 Topological groups, lie groups::22A Topological and differentiable algebraic systems Classificació AMS::46 Associative rings and algebras::46A Topological linear spaces and related structures Classificació AMS::54 General topology::54H Connections with other structures, applications |
| Sumario: | It is natural to extend the Grothendieck Theorem on completeness, valid for locally convex topological vector spaces, to abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, in this paper we present examples of metrizable locally quasi-convex groups for which the analogue to Grothendieck Theorem does not hold. By means of the continuous convergence structure on the dual of a topological group, we also state some weaker forms of Grothendieck Theorem valid for the class of locally quasi-convex groups. Finally, we prove that for the smaller class of nuclear groups, BB-reflexivity is equivalent to completeness. |
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