### Abstract

A family of sets has the (p,q) property if among any p members of the family some q have a nonempty intersection. It is shown that for every p ≥ q ≥ d+1 there is a c = c(p,q,d) < ∞ such that for every family F of compact, convex sets in R^{d} which has the (p,q) property there is a set of at most c points in R^{d} that intersects each member of F. This extends Helly's Theorem and settles an old problem of Hadwiger and Debrunner.

Original language | English (US) |
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Title of host publication | Eighth Annual Symposium On Computational Geometry |

Publisher | Publ by ACM |

Pages | 157-160 |

Number of pages | 4 |

ISBN (Print) | 0897915178, 9780897915175 |

DOIs | |

State | Published - 1992 |

Externally published | Yes |

Event | Eighth Annual Symposium On Computational Geometry - Berlin, Ger Duration: Jun 10 1992 → Jun 12 1992 |

### Publication series

Name | Eighth Annual Symposium On Computational Geometry |
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### Other

Other | Eighth Annual Symposium On Computational Geometry |
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City | Berlin, Ger |

Period | 6/10/92 → 6/12/92 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

Alon, N., & Kleitman, D. J. (1992). Piercing convex sets. In

*Eighth Annual Symposium On Computational Geometry*(pp. 157-160). (Eighth Annual Symposium On Computational Geometry). Publ by ACM. https://doi.org/10.1145/142675.142711