ABSTRACT
Helly’s Theorem reads: let C be a family of compact convex sets in ; if every n+1 of the sets in C have a common point, then all the family has a common point. Hadwiger showed that an extra hypothesis is needed to prove an analogous theorem for “lines that cross” convex sets in the plane. Hadwiger’s Theorem, [7], can be stated as follows. Let {C 1, C 2,…,C n } be a finite collection of convex sets in the plane such that for any three, C i , C j , C k , i<j<k, there is a line crossing them precisely in that order; then there exists a line crossing all the sets in the collection.
