Copyright © 2012 Ali Taghavi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using methods from the theory of commutative graded Banach algebras, we obtain a generalization of the two-dimensional Borsuk-Ulam theorem as follows. Let be a homeomorphism of order , and let be an th root of the unity, then, for every complex valued continuous function on , the function must vanish at some point of . We also discuss some noncommutative versions of the Borsuk-Ulam theorem.