Geodesic
An inverse theorem on `economic' maps
Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 554-568 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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S. I. Bogataya; S. A. Bogatyi; E. A. Kudryavtseva. An inverse theorem on `economic' maps. Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 554-568. http://geodesic.mathdoc.fr/item/SM_2012_203_4_a4/

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