Pontryagin reflexive groups are not determined by their continuous characters
A theorem of Glicksberg states that, for an abelian group G, two locally compact topologies with the same set of continuous characters must coincide. In [12] it is asserted that this fact also holds for two Pontryagin reflexive topologies. We prove here that this statement is not correct, and we giv...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 1998 |
| País: | España |
| Recursos: | Universidad de Navarra |
| Repositório: | Dadun. Depósito Académico Digital de la Universidad de Navarra |
| Idioma: | inglês |
| OAI Identifier: | oai:dadun.unav.edu:10171/58504 |
| Acesso em linha: | https://hdl.handle.net/10171/58504 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Continuous theorem Reflexive space Compact-open topology Pontryagin duality Glicksberg theorem Montel space |
| Resumo: | A theorem of Glicksberg states that, for an abelian group G, two locally compact topologies with the same set of continuous characters must coincide. In [12] it is asserted that this fact also holds for two Pontryagin reflexive topologies. We prove here that this statement is not correct, and we give some additional conditions under which it is true. We provide some examples of classes of groups determined by their continuous characters. |
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