An Elementary Deduction of the Topological Radon Theorem from Borsuk-Ulam

Abstract. The Topological Radon Theorem states that, for every continuous function from the boundary of a (d + 1)-dimensional simplex into Rn , there exist a pair of disjoint faces in the domain whose images intersect in Rn . The similarity between that result and the classical Borsuk-Ulam Theorem is unmistakeable, but a proof that the Topological Radon Theorem follows from Borsuk-Ulam is not immediate. In this note we provide an elementary argument verifying that implication.

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: Craig R. Guilbault
• Keywords: Classical Borsuk-ulam Theorem, Computer Graphics, Continuous Function, DCG 2010, Topological Radon Theorem