Open AccessOn strongly reflexive topological groups
Author(s) -
M.J. Chasco,
Elena Martín-Peinador
Publication year - 2001
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2001.2151
Subject(s) - mathematics , hausdorff space , metrization theorem , quotient , abelian group , combinatorics , topological group , group (periodic table) , quotient group , pure mathematics , duality (order theory) , cardinality (data modeling) , discrete mathematics , topology (electrical circuits) , cyclic group , mathematical analysis , separable space , chemistry , organic chemistry , computer science , data mining
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