Biblioteca de la Universidad Complutense de Madrid

An approach to duality on abelian precompact groups

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Chasco, M.J. y Martín Peinador, Elena (2008) An approach to duality on abelian precompact groups. Journal of Group Theory, 11 (5). pp. 635-643. ISSN 1435-4446

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Resumen

We prove that every dense subgroup of a topological abelian group has the same ‘convergence dual’ as the whole group. By the ‘convergence dual’ we mean the character group endowed with the continuous convergence structure. We draw as a corollary that the continuous
convergence structure on the character group of a precompact group is discrete and therefore a non-compact precompact group is never reflexive in the sense of convergence. We do not know if the same statement holds also for reflexivity in the sense of Pontryagin; at least in the category of metrizable abelian groups it does.


Tipo de documento:Artículo
Palabras clave:Pontryagin duality; Compact
Materias:Ciencias > Matemáticas > Topología
Código ID:12711
Depositado:13 May 2011 11:16
Última Modificación:06 Feb 2014 09:30

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