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  • On transversal group topologies
    Dikranjan, Dikran N., 1950- ; Tkachenko, Mikhail ; Yaschenko, Ivan
    Two non-discrete Hausdorff group topologies ▫$\tau_1, \tau_2$▫ on a group ▫$G$▫ are called transversal if the least upper bound ▫$\tau_1 \lor \tau_2$▫ of ▫$\taut_1$▫ and ▫$t_2$▫ is the discrete ... topology. We show that an infinite totally bounded topological group never admits a transversal group topology and we obtain a new criterion for precompactness in lattice-theoretical terms (the existence of transversal group topologies) for a large class of Abelian groups containing all divisible and all finitely generated groups. A full description is given of the class ▫$\mathfrak{M}$▫ of all abstract Abelian groups ▫$G$▫ where this criterion is valid (i.e., when the non-precompact group topologies on ▫$G$▫ are precisely the transversable ones). It turns out that ▫$\mathfrak{M}$▫ is the class of groups ▫$G$▫ for which the submaximal topology is precompact. We also give a complete description of the structure of the transversable locally compact Abelian groups.
    Vir: The Fifth Iberoamerican conference on topology and its applications (V CITA) : Lorca, Spain, 10-14 June 2003 (Str. 786-817)
    Vrsta gradiva - prispevek na konferenci
    Leto - 2005
    Jezik - angleški
    COBISS.SI-ID - 14085721

    Povezava(-e):

    http://dx.doi.org/10.1016/j.topol.2005.01.011

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