$F_\sigma$–additive families and the invariance of Borel classes
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Abstract:
We prove that any $F_\sigma$–additive family $\mathcal {A}$ of sets in an absolutely Souslin metric space has a $\sigma$–discrete refinement provided every partial selector set for $\mathcal {A}$ is $\sigma$–discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps $F_\sigma$–sets to $F_\sigma$–sets and has complete fibers, admits a section of the first class. The invariance of Borel and Souslin sets under mappings with complete fibers, which preserves $F_\sigma$-sets, is shown as an application of the previous result.References
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Additional Information
- Jiří Spurný
- Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
- Email: spurny@karlin.mff.cuni.cz
- Received by editor(s): April 10, 2003
- Received by editor(s) in revised form: October 30, 2003
- Published electronically: September 20, 2004
- Additional Notes: This research was supported in part by the grant GA ČR 201/03/0935, GA ČR 201/03/D120 and in part by the Research Project MSM 1132 00007 from the Czech Ministry of Education
- Communicated by: Alan Dow
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 905-915
- MSC (2000): Primary 54H05, 54E40; Secondary 28A05
- DOI: https://doi.org/10.1090/S0002-9939-04-07587-2
- MathSciNet review: 2113943