Stratification of families of functions definable in o-minimal structures (Q1873630)
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scientific article; zbMATH DE number 1916903
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stratification of families of functions definable in o-minimal structures |
scientific article; zbMATH DE number 1916903 |
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Stratification of families of functions definable in o-minimal structures (English)
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13 November 2003
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The author gives a short and elegant proof of the existence of Thom stratifications for families of functions definable in any o-minimal structure on the real field. As a corollary he obtains an extension of a result of \textit{T. Fukuda} [Publ. Math., Inst. Hautes Étud. Sci. 46, 87-106 (1976; Zbl 0341.57019)] on the number of topological types of polynomial functions on \(\mathbb R\) of bounded degree.
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Thom stratification
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o-minimal structure
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semialgebraic set
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definable set
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isotopy lemma
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