Geodesic
Continuous selections of multivalued maps with non-convex non-closed decomposable values
Sbornik. Mathematics, Tome 187 (1996) no. 5, pp. 745-766

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

A class of multivalued maps with non-convex non-closed decomposable values is distinguished, and theorems are proved on the existence of continuous selections for such maps. This class contains multivalued maps whose values are extreme points of continuous multivalued maps with closed convex decomposable values in a Banach space of Bochner-integrable functions. The proofs are based on the Baire category theorem. It is known that the set of extreme points of a closed convex set is in general not closed. Hence the results or paper answer the question of the existence of continuous selections for multivalued maps with non-convex non-closed values. 
@article{SM_1996_187_5_a6,
     author = {A. A. Tolstonogov},
     title = {Continuous selections of multivalued maps with non-convex non-closed decomposable values},
     journal = {Sbornik. Mathematics},
     pages = {745--766},
     publisher = {mathdoc},
     volume = {187},
     number = {5},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_5_a6/}
}
TY  - JOUR
AU  - A. A. Tolstonogov
TI  - Continuous selections of multivalued maps with non-convex non-closed decomposable values
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 745
EP  - 766
VL  - 187
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_5_a6/
LA  - en
ID  - SM_1996_187_5_a6
ER  - 
%0 Journal Article
%A A. A. Tolstonogov
%T Continuous selections of multivalued maps with non-convex non-closed decomposable values
%J Sbornik. Mathematics
%D 1996
%P 745-766
%V 187
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1996_187_5_a6/
%G en
%F SM_1996_187_5_a6
A. A. Tolstonogov. Continuous selections of multivalued maps with non-convex non-closed decomposable values. Sbornik. Mathematics, Tome 187 (1996) no. 5, pp. 745-766. http://geodesic.mathdoc.fr/item/SM_1996_187_5_a6/