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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, Number 1, Pages 101–112 (Mi basm356)  

This article is cited in 2 scientific papers (total in 2 papers)

Research articles

On the number of group topologies on countable groups

V. I. Arnautova, G. N. Ermakovab

a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., MD-2028, Chisinau Moldova
b Transnistrian State University, 25 October str., 128, Tiraspol, 278000 Moldova

Abstract: If a countable group $G$ admits a non-discrete Hausdorff group topology, then the lattice of all group topologies of the group $G$ admits:
– continuum $c$ of non-discrete metrizable group topologies such that $\sup\{\tau_1,\tau_2\}$ is the discrete topology for any two of these topologies;
– two to the power of continuum of coatoms in the lattice of all group topologies.

Keywords and phrases: countable group, group topology, Hausdorff topology, basis of the filter of neighborhoods, number of group topologies, lattice of group topologies, Stone–Čech compacification.

Full text: PDF file (148 kB)
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Document Type: Article
MSC: 22A05
Received: 25.02.2014
Language: English

Citation: V. I. Arnautov, G. N. Ermakova, “On the number of group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 1, 101–112

Citation in format AMSBIB
\Bibitem{ArnErm14}
\by V.~I.~Arnautov, G.~N.~Ermakova
\paper On the number of group topologies on countable groups
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2014
\issue 1
\pages 101--112
\mathnet{http://mi.mathnet.ru/basm356}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Arnautov, G. N. Ermakova, “On the number of ring topologies on countable rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 1, 103–114  mathnet
    2. V. I. Arnautov, G. N. Ermakova, “Lattice of all topologies of countable module over countable rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, no. 2, 63–70  mathnet
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