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Proceedings of the American Mathematical Society
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
MathSciNet review: 0356005
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Abstract | References | Similar Articles | Additional Information

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?)

  • [1] David Blackwell, A Borel set not containing a graph, Ann. Math. Statist. 39 (1968), 1345–1347. MR 0229451 (37 #5025)
  • [2] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751 (36 #840)
  • [3] N. N. Luzin, Leçons sur les ensembles analytiques et leurs applications, Gauthier-Villars, Paris, 1930.
  • [4] P. Novikov, Sur les fonctions implicites mesurables $ B$, Fund. Math. 17 (1931), 8-25.
  • [5] W. Sierpiński, Sur deux complémentaries analytiques non séparables $ B$, Fund. Math. 17 (1931), 296-297.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0356005-7
PII: S 0002-9939(1974)0356005-7
Keywords: Analytic sets, coanalytic sets, Borel separable, first principle of separation
Article copyright: © Copyright 1974 American Mathematical Society