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The Topological Radon Theorem states that, for every continuous function from the boundary of a (d+1)-dimensional simplex into ℝn , there exists 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 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.

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