### Approximation theorems in o-minimal structures

Jesús Escribano
Source: Illinois J. Math. Volume 46, Number 1 (2002), 111-128.

#### 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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Primary Subjects: 03C64
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