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Mat. Sb. (N.S.), 1973, Volume 92(134), Number 1(9), Pages 135–141 (Mi msb3335)  

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

Axiomatics of the dimension of metric spaces

E. V. Shchepin


Abstract: In this paper we prove that there exists a unique function $\dim X$ which assigns to every finite-dimensional metric space $X$ an integer $dX$ such that the following axioms are satisfied.
Axiom 1. $dT^n=n$ $(T^n$ is an $n$-dimensional simplex). \smallskip
Axiom 2. $d\bigcup^\infty_iX_i=\max_idX_i$ if all $X_i$ are closed in $\bigcup^\infty_iX_i=X$. \smallskip
Axiom 3. For every $X$ there exists a finite open cover $\omega$ such that $dY\geqslant dX$ for every $\omega$-mapping $f\colon X\to Y$. \smallskip
Axiom 4. For every $X$ there exists a closed subset $A$ such that $dA<dX$ and $X\setminus A$ is not connected.
Bibliography: 2 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 21:1, 137–143

Bibliographic databases:

UDC: 513.83
MSC: Primary 54F45; Secondary 54E35
Received: 20.02.1973

Citation: E. V. Shchepin, “Axiomatics of the dimension of metric spaces”, Mat. Sb. (N.S.), 92(134):1(9) (1973), 135–141; Math. USSR-Sb., 21:1 (1973), 137–143

Citation in format AMSBIB
\Bibitem{Shc73}
\by E.~V.~Shchepin
\paper Axiomatics of the dimension of metric spaces
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 1(9)
\pages 135--141
\mathnet{http://mi.mathnet.ru/msb3335}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=334163}
\zmath{https://zbmath.org/?q=an:0277.54036}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 1
\pages 137--143
\crossref{https://doi.org/10.1070/SM1973v021n01ABEH002008}


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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. P. S. Aleksandrov, V. V. Fedorchuk, V. I. Zaitsev, “The main aspects in the development of set-theoretical topology”, Russian Math. Surveys, 33:3 (1978), 1–53  mathnet  crossref  zmath
    2. A. V. Arkhangel'skii, V. M. Tikhomirov, “Pavel Samuilovich Urysohn (1898–1924)”, Russian Math. Surveys, 53:5 (1998), 875–892  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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