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Mathematics of the USSR-Sbornik, 1973, Volume 19, Issue 4, Pages 615–626
DOI: https://doi.org/10.1070/SM1973v019n04ABEH001820 (Mi sm3071) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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

M. A. Shtan'ko
English version PDF (831 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/SM1973v019n04ABEH001820
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.
Received: 11.07.1972
Bibliographic databases:
Document Type: Article
UDC: 513.83
MSC: 57A15, 57A35
Language: English
Original paper language: Russian
Citation: M. A. Shtan'ko, “Approximation of compacta in $E^n$ in codimension greater than two”, 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 Math. USSR-Sb.
\yr 1973
\vol 19
\issue 4
\pages 615--626
\mathnet{http://mi.mathnet.ru//eng/sm3071}
\crossref{https://doi.org/10.1070/SM1973v019n04ABEH001820}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=339194}
\zmath{https://zbmath.org/?q=an:0257.57008}
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  • https://www.mathnet.ru/eng/sm/v132/i4/p625
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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