Approximation theorems in o-minimal structures

Jesús Escribano

doi:10.1215/ijm/1258136143

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Home > Journals > Illinois J. Math. > Volume 46 > Issue 1 > Article

Spring 2002 Approximation theorems in o-minimal structures

Jesús Escribano

Illinois J. Math. 46(1): 111-128 (Spring 2002). DOI: 10.1215/ijm/1258136143

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Abstract

We prove that, in any o-minimal structure, definable $C^r$ mappings can always be approximated by definable $C^{r+1}$ mappings. As an application we obtain definable triviality for pairs of definable proper submersions.

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Jesús Escribano. "Approximation theorems in o-minimal structures." Illinois J. Math. 46 (1) 111 - 128, Spring 2002. https://doi.org/10.1215/ijm/1258136143