On Helly's Theorem and the Axioms of Convexity

In 1913, E. Helly[i] has established: "When C₁, ..., 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.