A one-one selection theorem
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- by H. Sarbadhikari PDF
- Proc. Amer. Math. Soc. 97 (1986), 320-322 Request permission
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
- Siegfried Graf and R. Daniel Mauldin, Measurable one-to-one selections and transition kernels, Amer. J. Math. 107 (1985), no. 2, 407–425. MR 784290, DOI 10.2307/2374421
- 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
- R. Daniel Mauldin, One-to-one selections—marriage theorems, Amer. J. Math. 104 (1982), no. 4, 823–828. MR 667537, DOI 10.2307/2374207
Additional Information
- © Copyright 1986 American Mathematical Society
- 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