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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the failure of the first principle of separation for coanalytic sets


Author: Ashok Maitra
Journal: Proc. Amer. Math. Soc. 46 (1974), 299-301
MSC: Primary 54H05
DOI: https://doi.org/10.1090/S0002-9939-1974-0356005-7
MathSciNet review: 0356005
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Abstract: In this note we present a new example of a pair of disjoint coanalytic sets which are not Borel separable, i.e., coanalytic sets $D$ and $H$ such that $D \cap H = \phi$ and such that there is no Borel set $E$ for which $D \subseteq E$ and $E \cap H = \phi$.


References [Enhancements On Off] (What's this?)

  • David Blackwell, A Borel set not containing a graph, Ann. Math. Statist. 39 (1968), 1345–1347. MR 229451, DOI https://doi.org/10.1214/aoms/1177698260
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
  • N. N. Luzin, Leçons sur les ensembles analytiques et leurs applications, Gauthier-Villars, Paris, 1930. P. Novikov, Sur les fonctions implicites mesurables $B$, Fund. Math. 17 (1931), 8-25. W. Sierpiński, Sur deux complémentaries analytiques non séparables $B$, Fund. Math. 17 (1931), 296-297.

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Keywords: Analytic sets, coanalytic sets, Borel separable, first principle of separation
Article copyright: © Copyright 1974 American Mathematical Society