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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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Author: Tamás Mátrai
Journal: Proc. Amer. Math. Soc. 137 (2009), 1115-1125
MSC (2000): Primary 03E15; Secondary 54H05, 28A05
Published electronically: October 23, 2008
MathSciNet review: 2457453
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a $ G_{\delta}$ $ \sigma$-ideal $ \mathcal{I}$ of compact subsets of $ 2^{\omega}$ such that $ \mathcal{I}$ contains all the singletons but there is no dense $ G_{\delta}$ set $ D \subseteq 2^{\omega}$ such that $ \{K \subseteq D \colon K\textrm{ compact}\} \subseteq \mathcal{I}$. This answers a question of A. S. Kechris in the negative.


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Additional Information

Tamás Mátrai
Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda Street 13-15, H-1053 Budapest, Hungary
Address at time of publication: University of Toronto, 40 St. George Street, Toronto, Ontario, M5S 2E4, Canada
Email: matrait@renyi.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09615-9
PII: S 0002-9939(08)09615-9
Keywords: $G_{\delta }$ $\sigma $-ideal of compact sets, singleton, ideal extension, covering property
Received by editor(s): November 14, 2007
Received by editor(s) in revised form: March 9, 2008, and April 14, 2008
Published electronically: October 23, 2008
Additional Notes: This research was partially supported by the OTKA grants F 43620, K 49786, K 61600 and by the József Öveges Program of the National Office for Research and Technology.
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.