%0 Journal Article
%A Chasco, M.J.
%A Martín Peinador, Elena
%T An approach to duality on abelian precompact groups
%D 2008
%@ 1435-4446
%U https://hdl.handle.net/20.500.14352/49680
%X 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 continuousconvergence 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.
%~