Dual topologies on non-abelian groups
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadades
Títol
Dual topologies on non-abelian groupsData de publicació
2012-06Editor
ElsevierTipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.sciencedirect.com/science/article/pii/S0166864112000351Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
The 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 ... [+]
The 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. [-]
Publicat a
Topology and its Applications, Volume 159, Issue 9, June 2012Drets d'accés
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Apareix a les col.leccions
- MAT_Articles [745]
Elements relacionats
Mostrant elements relacionats per títol, autoria, creador i matèria.
-
Restrictions on maximal invariant subgroups implying solvability of finite groups
Beltrán, Antonio; shao, Changguo Springer Verlag (2018)Suppose that G and A are finite groups such that A acts coprimely on G via automorphisms. It is interesting to investigate the structure and properties of G when we impose some restrictions on its maximal A-invariant ... -
Fuzzy quasi-pseudometrics on algebraic structures
Sánchez, Iván; Sanchis López, Manuel Elsevier (2018-01)In this work we state a number of theorems about fuzzy (quasi-)pseudometrizable algebraic structures. Our most useful results are: (1) a fuzzy semitopological group whose topology is induced by a left-invariant fuzzy ... -
Contributions to the Bohr topology by W.W. Comfort
Hernández, Salvador; Remus, Dieter; Trigos, Javier Elsevier (2019)The important rôle that W. W. Comfort played in the study of the Bohr topology is described.