Carathéodory and Helly-numbers of convex-product-structures

Abstract

Let Ci and c 2 be the CaratModory-numbers of the convexity-structures ^ for X u respectivily ^2 for X 2 . It is shown that the CaratModory-number c of the convex-productstructure ^ ^2 for XL X X 2 satisfies the inequality c : -f c 2 -2 g c g d + c 2 ; c l9 c 2 ^ 2.