On strongly reflexive topological groups
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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2001 |
| Country: | España |
| Institution: | Universidad de Navarra |
| Repository: | Dadun. Depósito Académico Digital de la Universidad de Navarra |
| Language: | English |
| OAI Identifier: | oai:dadun.unav.edu:10171/58491 |
| Online Access: | https://hdl.handle.net/10171/58491 |
| Access Level: | Open access |
| Keyword: | Pontryagin duality theorem Dual group Reflexive group Almost metrizable group Čech-complete group Strongly reflexive group |
| Summary: | 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. |
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