Extending Baire Property by countably many sets
Author:
Piotr Zakrzewski
Journal:
Proc. Amer. Math. Soc. 129 (2001), 271278
MSC (2000):
Primary 03E35, 54E52; Secondary 28A05
Published electronically:
June 14, 2000
MathSciNet review:
1695095
Fulltext PDF Free Access
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Abstract: We prove that if ZFC is consistent so is ZFC + ``for any sequence of subsets of a Polish space there exists a separable metrizable topology on with , and Borel in for all .'' This is a category analogue of a theorem of Carlson on the possibility of extending Lebesgue measure to any countable collection of sets. A uniform argument is presented, which gives a new proof of the latter as well. Some consequences of these extension properties are also studied.
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Additional Information
Piotr Zakrzewski
Affiliation:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02097 Warsaw, Poland
Email:
piotrzak@mimuw.edu.pl
DOI:
http://dx.doi.org/10.1090/S0002993900055052
PII:
S 00029939(00)055052
Keywords:
Measure and category,
Borel sets,
Baire Property,
$\sigma$algebra,
$\sigma$ideal
Received by editor(s):
July 10, 1998
Received by editor(s) in revised form:
March 16, 1999
Published electronically:
June 14, 2000
Additional Notes:
The author was partially supported by KBN grant 2 P03A 047 09 and by the Alexander von Humboldt Foundation
Communicated by:
Carl G. Jockusch, Jr.
Article copyright:
© Copyright 2000
American Mathematical Society
