## Abstract

It is shown that for every k and every p≥q≥d+1 there is a c=c(k,p,q,d)<∞ such that the following holds. For every family ℋ whose members are unions of at most k compact convex sets in R^{ d} in which any set of p members of the family contains a subset of cardinality q with a nonempty intersection there is a set of at most c points in R^{ d} that intersects each member of ℋ. It is also shown that for every p≥q≥d+1 there is a C=C(p,q,d)<∞ such that, for every family[Figure not available: see fulltext.] of compact, convex sets in R^{ d} so that among and p of them some q have a common hyperplane transversal, there is a set of at most C hyperplanes that together meet all the members of[Figure not available: see fulltext.].

Original language | English (US) |
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Pages (from-to) | 245-256 |

Number of pages | 12 |

Journal | Discrete & Computational Geometry |

Volume | 13 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1995 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics