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A Banach algebraic Approach to the Borsuk-Ulam Theorem
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 n and
be an nth root of the unity, then for every complex valued
continuous function on the function must be vanished at some point of . We give a
generalization in term of action of compact groups. We also discuss about some
noncommutative versions of the Borsuk- Ulam theore
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