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 Funktsional. Anal. i Prilozhen., 2019, Volume 53, Issue 1, Pages 79–83 (Mi faa3516)

Brief communications

On the Borsuk–Ulam theorem for Lipschitz mappings in an infinite-dimensional space

B. D. Gel'manab

a Voronezh State University
b Peoples' Friendship University of Russia, Moscow

Abstract: The present paper is devoted to the study of the solvability and dimension of the solution set of the equation $A (x) = f (x)$ on the sphere of a Hilbert space, in the case when A is a closed surjective operator and f a Lipschitz odd mapping. This theorem is a certain "analogue" of the infinite-dimensional version of the Borsuk-Ulam theorem.

Keywords: Borsuk–Ulam theorem, surjective operator, contractive mappings, Lipschitz constant, topological dimension.

 Funding Agency Grant Number Russian Science Foundation 17-11-01168

DOI: https://doi.org/10.4213/faa3516

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Bibliographic databases:

UDC: 517.988.6

Citation: B. D. Gel'man, “On the Borsuk–Ulam theorem for Lipschitz mappings in an infinite-dimensional space”, Funktsional. Anal. i Prilozhen., 53:1 (2019), 79–83

Citation in format AMSBIB
\Bibitem{Gel19} \by B.~D.~Gel'man \paper On the Borsuk--Ulam theorem for Lipschitz mappings in an infinite-dimensional space \jour Funktsional. Anal. i Prilozhen. \yr 2019 \vol 53 \issue 1 \pages 79--83 \mathnet{http://mi.mathnet.ru/faa3516} \crossref{https://doi.org/10.4213/faa3516} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3909121} \elib{https://elibrary.ru/item.asp?id=37045028}