A Banach Algebraic Approach to the Borsuk‐Ulam Theorem

Ali Taghavi

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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 ϕ : S2 → S2 be a homeomorphism of order n, and let λ ≠ 1 be an nth root of the unity, then, for every complex valued continuous function f on S2, the function ∑i=0n−1λif(ϕi(x)) must vanish at some point of S2. We also discuss some noncommutative versions of the Borsuk‐Ulam theorem.

Date: 2012
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https://doi.org/10.1155/2012/729745

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:729745

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