On Lipschitz Mappings onto a Square

  • Jiří Matoušek
Part of the Algorithms and Combinatorics book series (AC, volume 14)


Recently Preiss [4] proved that every subset of the plane of a positive Lebesgue measure can be mapped onto a square by a Lipschitz map. In this note we give an alternative proof of this result, based on a well-known combinatorial lemma of Erdős and Szekeres. The validity of an appropriate generalization of this lemma into higher dimensions remains as an open problem.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jiří Matoušek
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic

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