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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2013, Number 2-3, Pages 17–26 (Mi basm341)  

This article is cited in 3 scientific papers (total in 3 papers)

On the number of metrizable 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 metrizable group topology $\tau_0$, then in the group $G$, there are:
– Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are incomparable;
– Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are comparable.

Keywords and phrases: countable group, group topology, Hausdorff topology, basis of the filter of neighbourhoods, number of group topologies, metrizable group topology.

Full text: PDF file (139 kB)
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Document Type: Article
MSC: 22A05
Received: 09.10.2012
Language: English

Citation: V. I. Arnautov, G. N. Ermakova, “On the number of metrizable group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2013, no. 2-3, 17–26

Citation in format AMSBIB
\Bibitem{ArnErm13}
\by V.~I.~Arnautov, G.~N.~Ermakova
\paper On the number of metrizable group topologies on countable groups
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2013
\issue 2-3
\pages 17--26
\mathnet{http://mi.mathnet.ru/basm341}


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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 group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 1, 101–112  mathnet
    2. 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
    3. 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
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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