Extending Baire Property by countably many sets

Author:
Piotr Zakrzewski

Journal:
Proc. Amer. Math. Soc. **129** (2001), 271-278

MSC (2000):
Primary 03E35, 54E52; Secondary 28A05

DOI:
https://doi.org/10.1090/S0002-9939-00-05505-2

Published electronically:
June 14, 2000

MathSciNet review:
1695095

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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, 02-097 Warsaw, Poland

Email:
piotrzak@mimuw.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-00-05505-2

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