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Discrete & Computational Geometry

, Volume 24, Issue 2–3, pp 345–354 | Cite as

Transversals for Families of Translates of a Two-Dimensional Convex Compact Set

  • R. N. Karasev

Abstract.

The following Theorem 1 gives an affirmative answer to Grünbaum's old question. Let F be a family of translates of a convex compact set KR 2 . If every two elements of F have a common point, then there exist three points A, B, C ∈R 2 such that every element of F contains some of these points.

Keywords

Common Point Convex Compact Affirmative Answer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • R. N. Karasev
    • 1
  1. 1.Yaroslavl State University, Sovetskaya Str. 14, Yaroslavl 150000, Russia r_n_karasev@mail.ruRU

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