• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

Обращение теоремы об “экономичных” отображениях

Математический сборник. 2012. Т. 203. № 4. С. 103-118.
Богатая С. И., Богатый С. А., Кудрявцева Е. А.

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.