Two remarks about analytic sets
نویسنده
چکیده
In this paper we give two results about analytic sets. The rst is a counterexample to a problem of Fremlin. We show that there exists ! 1 compact subsets of a Borel set with the property that no -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. In his book about Martin's Axiom [2] p. 61 D. H. Fremlin shows that, assuming MA, for any analytic set X and set A X of cardinality less than the continuum there exists a -compact set L such that A L X. ( compact means countable union of compact sets.) Here we show that the 1 in Lecture Notes in Mathematics, Springer-Verlag, 1401(1989), 68-72. 2 Research partially supported by the Netherlands organization for the advancement of pure research 3 Research partially supported by NSF grant MCS-8401711
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