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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the failure of the first principle of separation for coanalytic sets
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by Ashok Maitra PDF
Proc. Amer. Math. Soc. 46 (1974), 299-301 Request permission

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
  • David Blackwell, A Borel set not containing a graph, Ann. Math. Statist. 39 (1968), 1345–1347. MR 229451, DOI 10.1214/aoms/1177698260
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], 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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Additional Information
  • © Copyright 1974 American Mathematical Society
  • 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