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

http://projecteuclid.org/euclid.ijm/1258136143

Mathematical Reviews number (MathSciNet)
MR1936078

Zentralblatt MATH identifier
1010.03026

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality

Citation

Escribano, Jesús. Approximation theorems in o-minimal structures. Illinois Journal of Mathematics 46 (2002), no. 1, 111--128. http://projecteuclid.org/euclid.ijm/1258136143.