On strongly reflexive topological groups
Submitted: 2014-02-17
|Accepted: 2014-02-17
|Published: 2001-10-01
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Keywords:
Pontryagin duality theorem, Dual group, Reflexive group, Almost metrizable group
Supporting agencies:
Partially supported by D.G.I.C.Y.T. BFM 2000-0804-C03-01
Abstract:
An Abelian topological group G is strongly reflexive if every closed subgroup and every Hausdorff quotient of G and of its dual group Gâ‹€, 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.
