Chasco, M.J.Martín Peinador, Elena2023-06-202023-06-202008-091435-444610.1515/JGT.2008.039https://hdl.handle.net/20.500.14352/49680We 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.engjournal articlehttp://www.reference-global.com/loi/jgthopen access515.1Pontryagin dualityCompactTopología1210 Topología