Vol. 96, No. 1, 1981

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Partition numbers for trees and ordered sets

Robert Edward Jamison, II

Vol. 96 (1981), No. 1, 115–140

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.

Mathematical Subject Classification 2000
Primary: 52A01
Secondary: 05A17, 06A99
Received: 19 November 1979
Published: 1 September 1981
Robert Edward Jamison, II