Separation by ambivalent sets (Q1772944)
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scientific article; zbMATH DE number 2160517
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Separation by ambivalent sets |
scientific article; zbMATH DE number 2160517 |
Statements
Separation by ambivalent sets (English)
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22 April 2005
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A characterization of when two sets in \([0,1]\) can be separated by ambivalent sets is shown. Two applications to some proofs of known theorems are presented. In particular it is proved that for disjoint subsets \(A\), \(B\) the following conditions are equivalent: (i) \(A\) and \(B\) can be separated by ambivalent sets, (ii) \(A\) and \(B\) can be separated by a Baire 1 function, (iii) there is no perfect set \(K\) such that both \(A\) and \(B\) are dense in \(K\).
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\(G_{\delta }\)-set
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\(F_{\sigma }\)-set
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ambivalent set
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Baire 1 function
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