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Discrete & Computational Geometry

, Volume 5, Issue 4, pp 325–331 | Cite as

Countable decompositions ofR2 andR3

  • P. Erdős
  • P. Komjáth
Article

Abstract

If the continuum hypothesis holds,R2 is the union of countably many sets, none spanning a right triangle. Some partial results are obtained concerning the following conjecture of the first author:R2 is the union of countably many sets, none spanning an isosceles triangle. Finally, it is shown thatR3 can be colored with countably many colors with no monochromatic rational distance.

Keywords

Discrete Comput Geom Isosceles Triangle Continuum Hypothesis Density Zero Countable Collection 
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.

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • P. Erdős
    • 1
  • P. Komjáth
    • 2
    • 3
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary
  2. 2.Department of MathematicsLehigh UniversityBethlehemUSA
  3. 3.Department of Computer ScienceR. Eötvös UniversityBudapestHungary

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