Universally meager sets (Q2706595)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Universally meager sets |
scientific article |
Statements
Universally meager sets (English)
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20 March 2001
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measure and category
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Borel sets
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Baire property
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\(\sigma\)-algebra
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\(\sigma\)-ideal
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universally meager sets
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A subset \(A\) of a perfect (i.e., with no isolated points) Polish (i.e., separable, metrizable) topological space \(X\) is universally meager if every Borel isomorphic image of \(A\) in \(X\) is meager. The author gives various equivalent definitions emphasizing analogies with the universally null sets of reals. Also some interesting results have been proved, like: ``the product of two universally meager sets is universally meager'' -- an improvement of Grzegorck's theorem assuming CH.
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