INTERSECTION PROPERTIES OF BOXES IN Rd.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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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. Hellys 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 hd, n such that a family of boxes in d-space is n-pierceable whenever each of its k-membered subfamilies is n-pierceable. Author
- Theoretical Mathematics