An Elementary Deduction of the Topological Radon Theorem from Borsuk-Ulam
The Topological Radon Theorem states that, for every continuous function from the boundary of a (d+1)-dimensional simplex into a"e (n) , there exists a pair of disjoint faces in the domain whose images intersect in a"e (n) . The similarity between that result and the classical Borsuk-Ulam Theorem is unmistakable, 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.
topological radon theorem borsuk-ulam theorem radon's theorem