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On transversal group topologiesDikranjan, Dikran N., 1950- ; Tkachenko, Mikhail ; Yaschenko, IvanTwo 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 konferenciLeto - 2005Jezik - angleškiCOBISS.SI-ID - 14085721
Avtor
Dikranjan, Dikran N., 1950- |
Tkachenko, Mikhail |
Yaschenko, Ivan
Teme
matematika |
topologija |
operator zaprtja |
lokalno kompaktna Abelova grupa |
centralna podgrupa |
totalna omejenost |
popolnoma zaprta množica |
mathematics |
topology |
transversal topology |
locally compact Abelian group |
central subgroup |
totally bounded |
submaximal topology |
absolutely closed set
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Dikranjan, Dikran N., 1950- | 28252 |
Tkachenko, Mikhail | ![]() |
Yaschenko, Ivan | ![]() |
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