%0 Journal Article
%A Barrera, de la, Daniel
%T Q is not a Mackey group
%D 2014
%@ 0166-8641
%U https://hdl.handle.net/20.500.14352/33840
%X The aim of this paper is to prove that the usual topology in Q inherited from the real line is not a Mackey topology in the sense defined in [5]. To that end, we find a locally quasi-convex topology on Q/Z, the torsion group of T, which is strictly finer than the one induced by the euclidean topology of T. Nevertheless, both topologies on Q/Z admit the same character group. Since the property of being a Mackey group is preserved by LQC   quotients, we obtain that the usual topology in Q is not the finest compatible topology. In other words, there is a strictly finer locally quasi-convex topology on Q giving rise to the same dual group as Q with the usual topology. A wide class of countable subgroups of the torus T, which are not Mackey are also obtained ( Remark 3.7). Obviously, they are precompact, metrizable and locally quasi-convex groups.
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