Accession Number : AD0678318

Title :   INTERSECTION PROPERTIES OF BOXES IN Rd.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Danzer,Ludwig ; Grunbaum,Branko

Report Date : SEP 1968

Pagination or Media Count : 21

Abstract : A family of sets is called n-pierceable if there exists a set of n points such that each member of the family contains at least one of the points. Helly's theorem on intersections of convex sets concerns families of 1-pierceable sets. This note gives a complete solution to the following Helly-type problem: If d and n are positive integers, what is the least h = h(d, n) such that a family of boxes in d-space is n-pierceable whenever each of its k-membered subfamilies is n-pierceable. (Author)

Descriptors :   (*SET THEORY, *GRAPHICS), COMBINATORIAL ANALYSIS, CONVEX SETS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE