On strongly reflexive topological groups

M. J. Chasco, E. Martin-Peinador

Abstract

An Abelian topological group G is strongly reflexive if every closed subgroup and every Hausdorff quotient of G and of its dual group G, is reflexive.

In this paper we prove the following: the annihilator of a closed subgroup of an almost metrizable group is topologically isomorphic to the dual of the corresponding Hausdorff quotient, and an analogous statement holds for the character group of the starting group. As a consequence of this perfect duality, an almost metrizable group is strongly reflexive just if its Hausdorff quotients, as well as the Hausdorff quotients of its dual, are reflexive. The simplification obtained may be significant from an operative point of view.


Keywords

Pontryagin duality theorem; Dual group; Reflexive group; Almost metrizable group

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1. Final group topologies, Kac-Moody groups and Pontryagin duality
Helge Glöckner, Ralf Gramlich, Tobias Hartnick
Israel Journal of Mathematics  vol: 177  issue: 1  first page: 49  year: 2010  
doi: 10.1007/s11856-010-0038-5



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