Two remarks about analytic sets

  • Fons van Engelen
  • Kenneth Kunen
  • Arnold W. Miller
Conference paper

DOI: 10.1007/BFb0097332

Part of the Lecture Notes in Mathematics book series (LNM, volume 1401)
Cite this paper as:
van Engelen F., Kunen K., Miller A.W. (1989) Two remarks about analytic sets. In: Steprāns J., Watson S. (eds) Set Theory and its Applications. Lecture Notes in Mathematics, vol 1401. Springer, Berlin, Heidelberg

Abstract

In this paper we give two results about analytic sets. The first is a counterexample to a problem of Fremlin. We show that there exists ω1 compact subsets of a Borel set with the property that no σ-compact subset of the Borel set covers them. In the second section we prove that for any analytic subset A of the plane either A can be covered by countably many lines or A contains a perfect subset P which does not have three collinear points.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Fons van Engelen
    • 1
  • Kenneth Kunen
    • 2
  • Arnold W. Miller
    • 3
  1. 1.Vrÿe Universiteit Subfaculteit WiskundeAmsterdamThe Netherlands
  2. 2.Department of MathematicsUniversity of WisconsinMadison
  3. 3.Department of MathematicsUniversity of WisconsinMadison

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