Geodesic
A~version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps
Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 841-853

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This paper is devoted to the proof of the infinite-dimensional Borsuk-Ulam theorem for odd completely continuous multivalued maps with convex images which are defined on level sets of even functions. The results obtained in the paper are new even for single-valued maps. In the final section some applications of the theorem to analysis and differential equations are discussed. Bibliography: 12 titles.
Keywords: multivalued map, Borsuk-Ulam theorem, surjective operator, level set of a function, topological dimension. 
@article{SM_2016_207_6_a3,
     author = {B. D. Gel'man},
     title = {A~version of the infinite-dimensional {Borsuk-Ulam} theorem for multivalued maps},
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     number = {6},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_6_a3/}
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B. D. Gel'man. A~version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps. Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 841-853. http://geodesic.mathdoc.fr/item/SM_2016_207_6_a3/