On strongly reflexive topological groups

  1. Chasco, M. J. 1
  2. Martin-Peinador, E. 2
  1. 1 Universidad de Navarra
    info

    Universidad de Navarra

    Pamplona, España

    ROR https://ror.org/02rxc7m23

  2. 2 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
Applied general topology

ISSN: 1576-9402,  1989-4147

Any de publicació: 2001

Volum: 2

Número: 2

Pàgines: 219-226

Tipus: Article

DOI: 10.4995/AGT.2001.2151 DIALNET GOOGLE SCHOLAR lock_openAccés obert editor

Altres publicacions en: Applied general topology

Resum

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.

Fuente de los datos: Dialnet