Geodesic
On the Borsuk--Ulam theorem for Lipschitz mappings in an infinite-dimensional space
Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 1, pp. 79-83

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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. 
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     author = {B. D. Gel'man},
     title = {On the {Borsuk--Ulam} theorem for {Lipschitz} mappings in an infinite-dimensional space},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2019_53_1_a6/}
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B. D. Gel'man. On the Borsuk--Ulam theorem for Lipschitz mappings in an infinite-dimensional space. Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 1, pp. 79-83. http://geodesic.mathdoc.fr/item/FAA_2019_53_1_a6/