On Helly's Theorem and the Axioms of Convexity

Abstract

In 1913, E. Helly[i] has established: When C 1 , ..., C m are convex domains in an n-dimensional Euclidean space and every set of n+I of these domains have a common point, then there exists a point which is common to all the domains. Recently[6] this theorem has obtained an enhanced importance because of the numerous applications which it affords.