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Mat. Sb. (N.S.), 1973, Volume 90(132), Number 4, Pages 625–636 (Mi msb3071)  

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

Approximation of compacta in $E^n$ in codimension greater than two

M. A. Shtan'ko


Abstract: The following is proved.
Theorem. For a compactum of codimension greater than or equal to three lying in Euclidean space there exists an arbitrarily close approximation by a locally homotopically unknotted (1-ULC) imbedding.
A series of corollaries about approximation of imbeddings of manifolds and polyhedra is derived. A problem about Menger universal compacta is solved. The article contains the complete proof of previously announced results stated in the references.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 19:4, 615–626

Bibliographic databases:

UDC: 513.83
MSC: 57A15, 57A35
Received: 11.07.1972

Citation: M. A. Shtan'ko, “Approximation of compacta in $E^n$ in codimension greater than two”, Mat. Sb. (N.S.), 90(132):4 (1973), 625–636; Math. USSR-Sb., 19:4 (1973), 615–626

Citation in format AMSBIB
\Bibitem{Sht73}
\by M.~A.~Shtan'ko
\paper Approximation of compacta in $E^n$ in codimension greater than two
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 4
\pages 625--636
\mathnet{http://mi.mathnet.ru/msb3071}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=339194}
\zmath{https://zbmath.org/?q=an:0257.57008}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 4
\pages 615--626
\crossref{https://doi.org/10.1070/SM1973v019n04ABEH001820}


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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. M. A. Shtan'ko, “Approximation of imbeddings of manifolds in codimension one”, Math. USSR-Sb., 23:3 (1974), 456–466  mathnet  crossref  mathscinet  zmath
    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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