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Mat. Sb., 2012, Volume 203, Number 4, Pages 103–118 (Mi msb7578)  

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

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.

DOI: https://doi.org/10.4213/sm7578

Full text: PDF file (522 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:4, 554–568

Bibliographic databases:

Document Type: Article
UDC: 515.127.15
MSC: 54F45
Received: 15.05.2009 and 09.09.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Bogatyi, “Generic planes conjecture”, Moscow University Mathematics Bulletin, 67:5-6 (2012), 200–205  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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