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Sbornik: Mathematics, 2016, Volume 207, Issue 6, Pages 841–853
DOI: https://doi.org/10.1070/SM8588
(Mi sm8588)
 

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
References:
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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00468-а
16-01-00677-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant nos. 14-01-00468-a and 16-01-00677-a).
Received: 28.08.2015 and 14.12.2015
Bibliographic databases:
Document Type: Article
UDC: 517.988.63
MSC: Primary 47H04, 47H10; Secondary 54H25
Language: English
Original paper language: Russian
Citation: B. D. Gel'man, “A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps”, Sb. Math., 207:6 (2016), 841–853
Citation in format AMSBIB
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\paper A~version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps
\jour Sb. Math.
\yr 2016
\vol 207
\issue 6
\pages 841--853
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Linking options:
  • https://www.mathnet.ru/eng/sm8588
  • https://doi.org/10.1070/SM8588
  • https://www.mathnet.ru/eng/sm/v207/i6/p79
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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