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Mat. Sb. (N.S.), 1969, Volume 79(121), Number 3(7), Pages 433–443 (Mi msb3597)  

This article is cited in 2 scientific papers (total in 2 papers)

On a class of infinite-dimensional spaces

A. I. Vainshtein


Abstract: In the paper is given a new version of the Hurewicz–Wallman characterization of dimension. Analogously to P. S. Aleksandrov's definitions, $W$-infinite-dimensional and $S$-infinite-dimensional spaces are introduced. It is proved that $W$-infinite-dimensional spaces satisfy the heredity condition and the sum theorem. Also, mappings of infinite-dimensional spaces which increase dimension are investigated.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1969, 8:3, 409–418

Bibliographic databases:

UDC: 513.83
MSC: 54E35, 54E45, 54F45, 54D20
Received: 20.12.1968

Citation: A. I. Vainshtein, “On a class of infinite-dimensional spaces”, Mat. Sb. (N.S.), 79(121):3(7) (1969), 433–443; Math. USSR-Sb., 8:3 (1969), 409–418

Citation in format AMSBIB
\Bibitem{Vai69}
\by A.~I.~Vainshtein
\paper On~a~class of infinite-dimensional spaces
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 79(121)
\issue 3(7)
\pages 433--443
\mathnet{http://mi.mathnet.ru/msb3597}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=244968}
\zmath{https://zbmath.org/?q=an:0185.26703|0193.51304}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 8
\issue 3
\pages 409--418
\crossref{https://doi.org/10.1070/SM1969v008n03ABEH001280}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dennis J. Garity, “Property C and closed maps”, Topology and its Applications, 26:2 (1987), 125  crossref
    2. V. V. Fedorchuk, “Weakly infinite-dimensional spaces”, Russian Math. Surveys, 62:2 (2007), 323–374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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