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Статья

An inverse theorem on 'economic' maps

Sbornik Mathematics. 2012. Vol. 203. No. 4. P. 554-568.
Bogataya S., Bogatyi S., E.A.Kudryavtseva.

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 \(dn + n + 1)/(m - n - d)] + d from the theorem on 'economic' maps. Bibliography: 16 titles.