Geodesic
Generic planes conjecture
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 13-19 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove that for some special cases the set of all continuous mappings of an $n$-dimensional compactum in an $m$-dimensional Euclidean space such that the set of all $d$-dimensional planes having the cardinality of the preimage $\geq q$ has the dimension $\le qn-(q-d-1)(m-d)$, is dense. 
@article{VMUMM_2012_5_a2,
     author = {S. A. Bogatyi},
     title = {Generic planes conjecture},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {13--19},
     year = {2012},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a2/}
}
TY  - JOUR
AU  - S. A. Bogatyi
TI  - Generic planes conjecture
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2012
SP  - 13
EP  - 19
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a2/
LA  - ru
ID  - VMUMM_2012_5_a2
ER  - 
%0 Journal Article
%A S. A. Bogatyi
%T Generic planes conjecture
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2012
%P 13-19
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a2/
%G ru
%F VMUMM_2012_5_a2
S. A. Bogatyi. Generic planes conjecture. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 13-19. http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a2/

[1] Bogatyi S.A., “Finite-to-one maps”, Topol. and Appl., 155 (2008), 1876–1887 | DOI | MR

[2] Dubrovin B.A., Novikov S.P., Fomenko A.T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[3] Hurewicz W., “Über Abbildungen von endlichdimensionalen Räumen auf Teilmengen Cartesischer Räume”, Sitzungsber. Preuss. Akad. Wiss. Phys.-Math. Kl., 4 (1933), 754–768

[4] Tuncali M., Valov V., “On regularly branched maps”, Topol. and Appl., 145 (2004), 119–145 | DOI | MR

[5] Boltyanskii V.G., “Otobrazheniya kompaktov v evklidovy prostranstva”, Izv. AN SSSR. Ser. matem., 23 (1959), 871–892

[6] Bogatyi S.A., “Tsvetnaya teorema Tverberga”, Vestn. Mosk. un-ta. Matem. Mekhan., 1999, no. 3, 14–19

[7] Goodsell T., “Strong general position and Menger curves”, Topol. and Appl., 120 (2002), 47–55 | DOI | MR

[8] Bogatyi S.A., Vylov V.M., “Vlozheniya Robertsa i obraschenie transversalnoi teoremy Tverberga”, Matem. sb., 196:11 (2005), 33–52 | DOI | MR

[9] Bogataya S., Bogatyi S., Valov V., “Embedding of finite-dimensional compacta in Euclidean spaces”, Topol. and Appl., 159 (2012), 1670–1677 | DOI | MR

[10] Bogatyi S.A., “Gipoteza Borsuka, prepyatstvie Ryshkova, interpolyatsiya, approksimatsiya Chebysheva, transversalnaya teorema Tverberga, zadachi”, Tr. Matem. in-ta RAN, 239, 2002, 63–82

[11] Bogataya S.I., Bogatyi S.A., Kudryavtseva E.A., “Obraschenie teoremy ob “ekonomichnykh” otobrazheniyakh”, Matem. sb., 203:4 (2012), 103–118 | DOI | MR