Uncountable intersections of open sets under CPA

Authors:
Krzysztof Ciesielski and Janusz Pawlikowski

Journal:
Proc. Amer. Math. Soc. **132** (2004), 3379-3385

MSC (2000):
Primary 03E35; Secondary 03E17

DOI:
https://doi.org/10.1090/S0002-9939-04-07475-1

Published electronically:
June 2, 2004

MathSciNet review:
2073315

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Covering Property Axiom CPA , which holds in the iterated perfect set model, implies the following facts.

- If is an intersection of -many open sets of a Polish space and has cardinality continuum, then contains a perfect set.
- There exists a subset of the Cantor set which is an intersection of -many open sets but is not a union of -many closed sets.

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Additional Information

**Krzysztof Ciesielski**

Affiliation:
Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310

Email:
K_Cies@math.wvu.edu

**Janusz Pawlikowski**

Affiliation:
Department of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Email:
pawlikow@math.uni.wroc.pl

DOI:
https://doi.org/10.1090/S0002-9939-04-07475-1

Keywords:
Uncountable intersections of open sets.

Received by editor(s):
March 3, 2003

Received by editor(s) in revised form:
July 27, 2003

Published electronically:
June 2, 2004

Additional Notes:
The work of the first author was partially supported by NATO Grant PST.CLG.977652 and by a 2002/03 West Virginia University Senate Research Grant.

Communicated by:
Alan Dow

Article copyright:
© Copyright 2004
American Mathematical Society