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This article is cited in 2 scientific papers (total in 2 papers)
A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps
B. D. Gel'manab a Peoples Friendship University of Russia, Moscow
b Voronezh State University
Abstract:
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.
Received: 28.08.2015 and 14.12.2015
Citation:
B. D. Gel'man, “A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps”, Sb. Math., 207:6 (2016), 841–853
Linking options:
https://www.mathnet.ru/eng/sm8588https://doi.org/10.1070/SM8588 https://www.mathnet.ru/eng/sm/v207/i6/p79
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