An inverse theorem on 'economic' maps
| Autor: | Semeon Antonovich Bogatyi, S.I. Bogataya, Elena A. Kudryavtseva |
|---|---|
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Sbornik: Mathematics. 203:554-568 |
| ISSN: | 1468-4802 1064-5616 |
| DOI: | 10.1070/sm2012v203n04abeh004234 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|