Geodesic
An inverse theorem on `economic' maps
Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 554-568

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2012_203_4_a4,
     author = {S. I. Bogataya and S. A. Bogatyi and E. A. Kudryavtseva},
     title = {An inverse theorem on `economic' maps},
     journal = {Sbornik. Mathematics},
     pages = {554--568},
     publisher = {mathdoc},
     volume = {203},
     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_4_a4/}
}
TY  - JOUR
AU  - S. I. Bogataya
AU  - S. A. Bogatyi
AU  - E. A. Kudryavtseva
TI  - An inverse theorem on `economic' maps
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 554
EP  - 568
VL  - 203
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_4_a4/
LA  - en
ID  - SM_2012_203_4_a4
ER  - 
%0 Journal Article
%A S. I. Bogataya
%A S. A. Bogatyi
%A E. A. Kudryavtseva
%T An inverse theorem on `economic' maps
%J Sbornik. Mathematics
%D 2012
%P 554-568
%V 203
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2012_203_4_a4/
%G en
%F SM_2012_203_4_a4
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/