On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space

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. © 2019, Springer Science+Business Media, Inc.