Borel sets with countable sections for nonseparable spaces
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- by Petr Holický PDF
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Abstract:
We prove that every (extended) Borel subset $E$ of $X\times Y$, where $X$ is a complete metric and $Y$ is Polish, can be covered by countably many extended Borel graphs of mappings from $X$ to $Y$ if the sections $E_x=\{y\in Y:(x,y)\in E\}$, $x\in X$, are countable. This is a nonseparable version of a classical theorem of Luzin and Novikov.References
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Additional Information
- Petr Holický
- Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
- Email: holicky@karlin.mff.cuni.cz
- Received by editor(s): September 27, 2004
- Received by editor(s) in revised form: December 7, 2004
- Published electronically: October 6, 2005
- Additional Notes: This research was partially supported by grants GAČR 201/03/0933, GAČR 201/03/0931 and MSM 113200007
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1519-1525
- MSC (2000): Primary 54H05; Secondary 54C65, 28A05
- DOI: https://doi.org/10.1090/S0002-9939-05-08099-8
- MathSciNet review: 2199201