Email this article On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space
- Authors: Gel’man B.D.1,2
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Affiliations:
- Voronezh State University
- Peoples’ Friendship University of Russia
- Issue: Vol 53, No 1 (2019)
- Pages: 61-64
- Section: Brief Communications
- URL: https://journal-vniispk.ru/0016-2663/article/view/234700
- DOI: https://doi.org/10.1007/s10688-019-0249-4
- ID: 234700
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Abstract
The solvability of the equation A(x) = f(x) on the sphere of a Hilbert space and the dimension of its solution set are studied in the case where A is a closed surjective operator and f is an odd Lipschitz mapping. A kind of analogue of the infinite-dimensional version of the Borsuk-Ulam theorem is obtained.
About the authors
B. D. Gel’man
Voronezh State University; Peoples’ Friendship University of Russia
Author for correspondence.
Email: gelman_boris@mail.ru
Russian Federation, Voronezh; Moscow
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