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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 3(7), Pages 339–357 (Mi msb3686)  

This article is cited in 1 scientific paper (total in 1 paper)

Some theorems on the metrization of Abelian groups

V. K. Bel'nov


Abstract: The results of this paper are concerned with the construction of a metrizable topology $\nu$ on an infinite Abelian group $G$, compatible with the group structure, such that the completion $\nu G$ of the group $(G,\nu)$ is arcwise connected and locally arcwise connected.
As an application of these results, we describe a method by which any metrizable Abelian group of weight $\mathbf m$ can be imbedded as a closed subgroup of an arcwise connected and locally arcwise connected metrizable Abelian group of weight $\max(\mathbf m,\aleph_0)$.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:3, 319–335

Bibliographic databases:

UDC: 519.46
MSC: Primary 22A05; Secondary 20K45
Received: 20.02.1973

Citation: V. K. Bel'nov, “Some theorems on the metrization of Abelian groups”, Mat. Sb. (N.S.), 94(136):3(7) (1974), 339–357; Math. USSR-Sb., 23:3 (1974), 319–335

Citation in format AMSBIB
\Bibitem{Bel74}
\by V.~K.~Bel'nov
\paper Some theorems on the metrization of Abelian groups
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 3(7)
\pages 339--357
\mathnet{http://mi.mathnet.ru/msb3686}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=369596}
\zmath{https://zbmath.org/?q=an:0313.22001}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 3
\pages 319--335
\crossref{https://doi.org/10.1070/SM1974v023n03ABEH002180}


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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. M. I. Vishik, A. V. Fursikov, “The Cauchy problem for nonlinear Schrödinger-type equations”, Math. USSR-Sb., 25:3 (1975), 429–440  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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