Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2010, Number 2, Pages 3–19 (Mi basm255)  

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

Research articles

Properties of final unrefinable chains of groups topologies

V. I. Arnautov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova
Full-text PDF (344 kB) Citations (3)
References:
Abstract: Let $G$ be a nilpotent group and $(\mathfrak M,<)$ be the lattice of all group topologies or the lattice of all group topologies in each of which the group $G$ possesses a basis of neighborhood of unit consisting of subgroups. If $\tau$ and $\tau'$ are group topologies from $\mathfrak M$ such that $\tau=\tau_0\prec_\mathfrak M\tau_1\prec_\mathfrak M\ldots\prec_\mathfrak M\tau_n=\tau'$, then $k\leq n$ for any chain $\tau=\tau'_0<\tau'_1<\ldots<\tau'_k=\tau'$ of topologies from $\mathfrak M$.
Keywords and phrases: topological groups, lattice of group topologies, modular lattice, chain of topologies, unrefinable chain.
Received: 03.03.2010
Bibliographic databases:
Document Type: Article
MSC: 22A05
Language: English
Citation: V. I. Arnautov, “Properties of final unrefinable chains of groups topologies”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, no. 2, 3–19
Citation in format AMSBIB
\Bibitem{Arn10}
\by V.~I.~Arnautov
\paper Properties of final unrefinable chains of groups topologies
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2010
\issue 2
\pages 3--19
\mathnet{http://mi.mathnet.ru/basm255}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2743049}
\zmath{https://zbmath.org/?q=an:1204.22001}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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