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Mat. Sb., 2016, Volume 207, Number 6, Pages 79–92 (Mi msb8588)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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).


DOI: https://doi.org/10.4213/sm8588

Full text: PDF file (493 kB)
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English version:
Sbornik: Mathematics, 2016, 207:6, 841–853

Bibliographic databases:

UDC: 517.988.63
MSC: Primary 47H04, 47H10; Secondary 54H25
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”, Mat. Sb., 207:6 (2016), 79–92; Sb. Math., 207:6 (2016), 841–853

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. D. Gelman, “O teoreme Borsuka–Ulama dlya lipshitsevykh otobrazhenii v beskonechnomernom prostranstve”, Funkts. analiz i ego pril., 53:1 (2019), 79–83  mathnet  crossref  mathscinet  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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