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Sbornik: Mathematics, 2012, Volume 203, Issue 4, Pages 554–568
DOI: https://doi.org/10.1070/SM2012v203n04ABEH004234 (Mi sm7578) 		 
This article is cited in 1 scientific paper (total in 1 paper)

An inverse theorem on ‘economic’ maps

S. I. Bogatayaa, S. A. Bogatyib, E. A. Kudryavtsevab

a National Research University "Higher School of Economics"
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (311 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2012v203n04ABEH004234
Abstract: We prove that the bound from the theorem on ‘economic’ maps is best possible. Namely, for $m>n+d$ we construct a map from an $n$-dimensional simplex to an $m$-dimensional Euclidean space for which (and for any close map) there exists a $d$-dimensional plane whose preimage has cardinality not less than the upper bound $\lceil(dn+n+1)/(m-n-d)\rceil+d$ from the theorem on ‘economic’ maps.
Bibliography: 16 titles.
Keywords: embedding, Euclidean space, cardinality of the preimage of a plane.
Received: 15.05.2009 and 09.09.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 4, Pages 103–118
DOI: https://doi.org/10.4213/sm7578
Bibliographic databases:
Document Type: Article
UDC: 515.127.15
MSC: 54F45
Language: English
Original paper language: Russian
Citation: S. I. Bogataya, S. A. Bogatyi, E. A. Kudryavtseva, “An inverse theorem on ‘economic’ maps”, Mat. Sb., 203:4 (2012), 103–118; Sb. Math., 203:4 (2012), 554–568
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2012v203n04ABEH004234
  • https://www.mathnet.ru/eng/sm/v203/i4/p103
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:72
    First page:37
     
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