Notes About the Caratheodory Number
In this paper we give sufficient conditions for a compactum in a"e (n) to have Carath,odory number less than n+1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath,odory theorem and give a Tverberg-type theorem for families of convex compacta.
caratheodory's theorem helly's theorem tverberg's theorem