-additive families and the invariance of Borel classes

Author:
Jirí Spurny

Journal:
Proc. Amer. Math. Soc. **133** (2005), 905-915

MSC (2000):
Primary 54H05, 54E40; Secondary 28A05

Published electronically:
September 20, 2004

MathSciNet review:
2113943

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that any -additive family of sets in an absolutely Souslin metric space has a -discrete refinement provided every partial selector set for is -discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps -sets to -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 -sets, is shown as an application of the previous result.

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Additional Information

**Jirí Spurny**

Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Email:
spurny@karlin.mff.cuni.cz

DOI:
https://doi.org/10.1090/S0002-9939-04-07587-2

Keywords:
$F_\sigma$--additive family,
$\sigma$--discrete refinement,
first class selector,
Borel classes

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 GAČR 201/03/0935, GAČR 201/03/D120 and in part by the Research Project MSM 1132 00007 from the Czech Ministry of Education

Communicated by:
Alan Dow

Article copyright:
© Copyright 2004
American Mathematical Society