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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2010, Number 2, Pages 3–19
(Mi basm255)
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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
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
Citation:
V. I. Arnautov, “Properties of final unrefinable chains of groups topologies”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, no. 2, 3–19
Linking options:
https://www.mathnet.ru/eng/basm255 https://www.mathnet.ru/eng/basm/y2010/i2/p3
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Abstract page: | 283 | Full-text PDF : | 49 | References: | 60 |
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