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      Precompact groups and convergence

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          Abstract

          We consider precompact sequential and Fr\'echet group topologies and show that some natural constructions of such topologies always result in metrizable groups answering a question of D.~Dikranjan et al. We show that it is consistent that all sequential precompact topologies on countable groups are Fr\'echet (or even metrizable). For some classes of groups (for example boolean) extra set-theoretic assumptions may be omitted (although in this case such groups do not have to be metrizable). We also build (using \(\diamondsuit\)) an example of a countably compact Fr\'echet group that is not \(\alpha_3\) and obtain a counterexample to a conjecture of D.~Shakhmatov as a corollary.

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          Metrizability and the Fréchet-Urysohn property in topological groups

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            On sequential analytic groups

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              No interesting sequential groups

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                Author and article information

                Journal
                21 March 2019
                Article
                1903.09236
                34e4af2a-e592-409c-9f56-a7904f98028f

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.GN

                Geometry & Topology
                Geometry & Topology

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