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Proceedings of the American Mathematical Society

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A one-one selection theorem


Author: H. Sarbadhikari
Journal: Proc. Amer. Math. Soc. 97 (1986), 320-322
MSC: Primary 54C65; Secondary 03E15, 04A15
DOI: https://doi.org/10.1090/S0002-9939-1986-0835890-4
MathSciNet review: 835890
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Abstract: Let $ X$, $ Y$ be Polish spaces without isolated points and $ B \subseteq X \times Y$ a Borel set such that $ x:{B_x}$ is nonmeager is comeager in $ X$ and $ y:{B^y}$ is nonmeager is comeager in $ Y$. There is a comeager Borel $ E \subseteq X$, a comeager Borel $ F \subseteq Y$ and a Borel isomorphism $ f$ from $ E$ onto $ F$ such that graph of $ f \subseteq B$.


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

  • [1] S. Graf and R. D. Mauldin, Measurable one-to-one selections and transition kernels, Amer. J. Math. (to appear). MR 784290 (86e:54044)
  • [2] K. Kuratowski, Topology, Vol. I, Academic Press, New York; PWN, Warsaw, 1966. MR 0217751 (36:840)
  • [3] R. D. Mauldin, One-to-one selections--marriage theorems, Amer. J. Math. 104 (1982), 823-828. MR 667537 (84b:28013)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0835890-4
Keywords: Comeager set, Borel isomorphism, graph of a function
Article copyright: © Copyright 1986 American Mathematical Society

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