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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 5, Pages 961–973 (Mi smj924)  
This article is cited in 2 scientific papers (total in 2 papers)

On coverings in the lattice of all group topologies of arbitrary Abelian groups

V. I. Arnautov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova
Full-text PDF (228 kB) Citations (2)
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Abstract: The remainder of the completion of a topological abelian group $(G,\tau_0)$ contains a nonzero element of prime order if and only if $G$ admits a Hausdorff group topology $\tau_1$ that precedes the given topology and is such that $(G,\tau_0)$ has no base of closed zero neighborhoods in $(G,\tau_1)$.
Keywords: abelian group, group topology, lattice of topologies, covering, preceding topology, completion.
Received: 09.03.2005
English version:
Siberian Mathematical Journal, 2006, Volume 47, Issue 5, Pages 787–796
DOI: https://doi.org/10.1007/s11202-006-0089-3
Bibliographic databases:
UDC: 512.546.2
Language: Russian
Citation: V. I. Arnautov, “On coverings in the lattice of all group topologies of arbitrary Abelian groups”, Sibirsk. Mat. Zh., 47:5 (2006), 961–973; Siberian Math. J., 47:5 (2006), 787–796
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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