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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 \emph {no} dense G_{\delta } set D \subseteq 2^{\omega } such that \{K \subseteq D \colon K\textrm { compact}} \subseteq \mathcal {I}. This answers...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2009-03, Vol.137 (3), p.1115-1125
Main Author: MATRAI, Tamas
Format: Article
Language:English
Subjects:
Descriptive set theory
Exact sciences and technology
General mathematics
General, history and biography
Homeomorphism
Mathematical theorems
Mathematics
Sciences and techniques of general use
Topological spaces
Topological theorems
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Summary: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 \emph {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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-08-09615-9