Symmetries of two-point sets

  title={Symmetries of two-point sets},
  author={Ben Chad and Rolf Suabedissen},
  • Ben Chad, Rolf Suabedissen
  • Published 2008
A two-point set is a subset of the plane which meets every planar line in exactly two-points. We discuss the problem “What are the topological symmetries of a twopoint set?”. Our main results assert the existence of two-point sets which are rigid and the existence of two-point sets which are invariant under the action of certain autohomeomorphism groups. We pay particular attention to the isometry group of a two-point set, and show that such groups consist only of rotations and that they may be… CONTINUE READING

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