An Infinite-Dimensional Version of the Borsuk-Ulam Theorem

Author： Gel’man B.  

Publisher： Springer Publishing Company

ISSN： 0016-2663

Source： Functional Analysis and Its Applications, Vol.38, Iss.4, 2004-10, pp. : 239-242

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Abstract

We study the solvability of the equation a(x) = f(x) on a sphere in a Banach space, where a is a closed surjective linear operator and f is an odd a-compact map. We also estimate the topological dimension of the solution set and give applications of the corresponding theorem to some problems in differential equations and other fields of mathematics.

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