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Completeness properties of locally quasi-convex groups
Bruguera Padró, Mª Montserrat; Chasco Ugarte, Maria Jesús; Martín Peinador, Elena; Tarieladze, V. I. (Vazha Izemovich)
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
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.
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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