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oai:docta.ucm.es:20.500.14352/338402023-08-11T06:00:48Zcom_20.500.14352_14col_20.500.14352_15

Q is not a Mackey group Barrera, de la, Daniel 51 Locally quasi-convex Mackey topology Dual group Matemáticas (Matemáticas) 12 Matemáticas 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. MICINN Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-19T13:29:10Z 2023-06-19T13:29:10Z 2014-12 journal article https://hdl.handle.net/20.500.14352/33840 0166-8641 10.1016/j.topol.2014.10.004 eng MTM2009-14409-C02-01 restricted access application/pdf Elsevier