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Archiv der Mathematik

, Volume 80, Issue 6, pp 664–672 | Cite as

A Helly theorem for intersections of orthogonally starshaped sets

  • Marilyn Breen
Original paper

Abstract.

Let $\cal{F}$ be a finite family of simply connected orthogonal polygons in the plane. If every three (not necessarily distinct) members of $\cal{F}$ have a nonempty intersection which is starshaped via staircase paths, then the intersection $\cap \{F : F\; \hbox{in}\; \cal{F}\}$ is a (nonempty) simply connected orthogonal polygon which is starshaped via staircase paths. Moreover, the number three is best possible, even with the additional requirement that the intersection in question be nonempty. The result fails without the simple connectedness condition.

Mathematics Subject Classification (2000):

Primary 52A30 52A35 

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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  • Marilyn Breen
    • 1
  1. 1.Department of MathematicsUniversity of OklahomaNormanUSA

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