o-minimal analytic separation of sets in dimension 2 (Q1006609)
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scientific article; zbMATH DE number 5532835
| Language | Label | Description | Also known as |
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| English | o-minimal analytic separation of sets in dimension 2 |
scientific article; zbMATH DE number 5532835 |
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o-minimal analytic separation of sets in dimension 2 (English)
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25 March 2009
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The author proves the very interesting theorem that definable analytic separation of definable sets in the plane is equivalent with density of definable analytic germs in the Hardy field \(H_{\mathcal{M}}\). This result is a generalization in dimension \(2\) of the famous separation theorem of \textit{T. Mostowski} [``Some properties of the ring of Nash functions'', Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 3, 245--266 (1976; Zbl 0335.14001)].
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o-minimal structure
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analytic separation
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Hardy field
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