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Nash constructible functions

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Abstract.

Nash constructible functions on a real algebraic set V are defined as linear combinations, with integer coefficients, of Euler characteristic of fibres of proper regular morphisms restricted to connected components of algebraic sets. We prove that if V is compact, these functions are sums of signs of semialgebraic arc-analytic functions (i.e. functions which become analytic when composed with any analytic arc). We also give a sharp upper bound to the number of semialgebraic arc-analytic functions which are necessary to define any given Nash constructible functions.

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  1. Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013, Paris, France

    Isabelle Bonnard

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  1. Isabelle Bonnard
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Correspondence to Isabelle Bonnard.

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Bonnard, I. Nash constructible functions. manuscripta math. 112, 55–75 (2003). https://doi.org/10.1007/s00229-003-0391-3

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  • DOI: https://doi.org/10.1007/s00229-003-0391-3

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