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