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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 3(7), Pages 483–494 (Mi msb3694)  

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

Approximation of imbeddings of manifolds in codimension one

M. A. Shtan'ko


Abstract: It is shown that any $(n-1)$-manifold topologically imbedded in a Euclidean space of dimension greater than four can be approximated arbitrarily closely by one whose complement has the property of uniform local one-connectedness.
From this theorem and the results of Chernavskii and Kirby–Siebenmann it is deduced that there also exists a piecewise linear approximation if the dimension of the Euclidean space is greater than five.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:3, 456–466

Bibliographic databases:

UDC: 513.83
MSC: Primary 57A35; Secondary 57C35, 57C55
Received: 08.01.1974

Citation: M. A. Shtan'ko, “Approximation of imbeddings of manifolds in codimension one”, Mat. Sb. (N.S.), 94(136):3(7) (1974), 483–494; Math. USSR-Sb., 23:3 (1974), 456–466

Citation in format AMSBIB
\Bibitem{Sht74}
\by M.~A.~Shtan'ko
\paper Approximation of imbeddings of manifolds in codimension one
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 3(7)
\pages 483--494
\mathnet{http://mi.mathnet.ru/msb3694}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=370596}
\zmath{https://zbmath.org/?q=an:0315.57005}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 3
\pages 456--466
\crossref{https://doi.org/10.1070/SM1974v023n03ABEH001726}


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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. J.W. Cannon, “Taming codimension—One generalized submanifolds of Sn”, Topology, 16:4 (1977), 323  crossref
    2. A. V. Chernavskii, “On the work of L. V. Keldysh and her seminar”, Russian Math. Surveys, 60:4 (2005), 589–614  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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