Partition numbers for trees and ordered sets

Abstract

In this paper some bounds on the Tveberg-type convexity partition numbers of abstract spaces will be presented. The main objective is to show that a conjecture of J. Eckhoff relating the Tverberg numbers to the Radon number is valid for a certain class of spaces which include ordered sets, trees, pairwise products of trees and subspaces of these. (Application of the Main Theorem to a certain class of semilattices is given in an appendix.) For ordered sets the results here improve those of P. W. Bean and are best possible for general ordered sets.