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Proceedings of the American Mathematical Society

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

 
 

 

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$.


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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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