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dc.contributor.authorFerrer González, María Vicenta
dc.contributor.authorHernández Muñoz, Salvador
dc.date.accessioned2013-05-15T10:11:12Z
dc.date.available2013-05-15T10:11:12Z
dc.date.issued2012-06
dc.identifier.urihttp://hdl.handle.net/10234/63519
dc.description.abstractThe notion of locally quasi-convex abelian group, introduced by Vilenkin, is extended to maximally almost periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set rep(G)rep(G) of all finite dimensional continuous representations on a topological group G in order to associate well behaved group topologies (dual topologies) to them. As a consequence, the poset of all Hausdorff totally bounded group topologies on a group G is shown to be isomorphic to the poset of certain special subsets of rep(Gd)rep(Gd). Moreover, generalizing some ideas of Namioka, we relate the structural properties of the dual topological groups to topological properties of the bounded subsets belonging to the associate bornology. In like manner, certain type of bornologies that can be defined on a group G allow one to define canonically associate uniformities on the dual object View the MathML sourceGˆ. As an application, we prove that if for every dense subgroup H of a compact group G we have that if View the MathML sourceHˆ and View the MathML sourceGˆ are uniformly isomorphic, then G is metrizable. Thereby, we extend to non-abelian groups some results previously considered for abelian topological groups.ca_CA
dc.format.extent10 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherElsevierca_CA
dc.relation.isPartOfTopology and its Applications, Volume 159, Issue 9, June 2012ca_CA
dc.subjectCompact groupca_CA
dc.subjectMaximally almost periodic groupca_CA
dc.subjectTotally bounded groupca_CA
dc.subjectκ-Narrow groupca_CA
dc.subjectκ-Narrow uniform spaceca_CA
dc.subjectLindelöf numberca_CA
dc.subjectDetermined groupca_CA
dc.subjectTannaka–Kreı̌n dualityca_CA
dc.subjectDual topological groupca_CA
dc.titleDual topologies on non-abelian groupsca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttp://dx.doi.org/10.1016/j.topol.2011.08.031
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.relation.publisherVersionhttp://www.sciencedirect.com/science/article/pii/S0166864112000351ca_CA


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