We present an extension of Borsuk's antipodal theorem (existence of a zero) for antipodally approachable correspondences without convex values. This result is a generalization of Borsuk-Ulam Theorem and has a fixed-point equivalent formulation.

This short paper, published in Games and Economic Behavior (July 2009) "In Memoriam" of David Gale, emphasizes the seminal role played by two lemmas of David Gale in the development of the foundations of General Equilibrium Theory.