Set Theory and its Applications

Volume 1401 of the series Lecture Notes in Mathematics pp 68-72


Two remarks about analytic sets

  • Fons van EngelenAffiliated withVrÿe Universiteit Subfaculteit Wiskunde
  • , Kenneth KunenAffiliated withDepartment of Mathematics, University of Wisconsin
  • , Arnold W. MillerAffiliated withDepartment of Mathematics, University of Wisconsin

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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.