# 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):

# Report Date:

## 1968-09-01

# Pagination or Media Count:

## 21.0

# 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. 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics