Illinois Journal of Mathematics

Approximation theorems in o-minimal structures

Jesús Escribano

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.

Article information

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

Dates
First available in Project Euclid: 13 November 2009