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Borel sets with countable sections for nonseparable spaces

Author: Petr Holicky
Journal: Proc. Amer. Math. Soc. 134 (2006), 1519-1525
MSC (2000): Primary 54H05; Secondary 54C65, 28A05
Published electronically: October 6, 2005
MathSciNet review: 2199201
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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.

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Additional Information

Petr Holicky
Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic

Keywords: Extended Borel sets, countable sections, nonseparable metric spaces
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.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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