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An approach to duality on abelian precompact groups

Chasco, M.J. and 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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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Pontryagin duality; Compact
Subjects:Sciences > Mathematics > Topology
ID Code:12711
Deposited On:13 May 2011 11:16
Last Modified:06 Feb 2014 09:30

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