RT Journal Article
T1 A survey on reflexivity of abelian topological groups
A1 Chasco, M.J.
A1 Dikranjan, Dikran
A1 Martín Peinador, Elena
AB The Pontryagin duality theorem for locally compact abelian groups (briefly, LCA groups) has been the starting point for many different routes of research in Mathematics. From its appearance there was a big interest to extend it in a context broader than LCA groups. Kaplan in the 40ʼs proposed—and it still remains open—the problem of characterization of all abelian topological groups for which the canonical mapping into its bidual is a topological isomorphism, assuming that the dual and the bidual carry the compact-open topology. Such groups are called reflexive.In this survey we deal with results on reflexivity of certain classes of groups, with special emphasis on the smaller class which better reflects the properties of LCA groups, namely that of strongly reflexive groups. A topological abelian group is said to be strongly reflexive if all its closed subgroups and its Hausdorff quotients as well as the closed subgroups and the Hausdorff quotients of its dual group are reflexive.
PB Elsevier Science
SN 0166-8641
YR 2012
FD 2012-06
LK https://hdl.handle.net/20.500.14352/42300
UL https://hdl.handle.net/20.500.14352/42300
LA eng
NO Ministerio de Ciencia e Innovación
DS Docta Complutense
RD 17 abr 2025