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...

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Detalles Bibliográficos
Autores: Martin-Peinador, E. (E.)|||/items/a50833c3-5aaf-4de2-a2ba-c5af3f8123fe, Chasco, M.J. (María Jesús)|||/items/1a5675d0-b528-49b9-8e76-ad17aa596eb9
Tipo de recurso: artículo
Fecha de publicación:1998
País:España
Institución:Universidad de Navarra
Repositorio:Dadun. Depósito Académico Digital de la Universidad de Navarra
Idioma:inglés
OAI Identifier:oai:dadun.unav.edu:10171/58504
Acceso en línea:https://hdl.handle.net/10171/58504
Access Level:acceso abierto
Palabra clave:Continuous theorem
Reflexive space
Compact-open topology
Pontryagin duality
Glicksberg theorem
Montel space
Descripción
Sumario: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.