O-minimal version of Whitney's extension theorem (Q2928195)

In the paper under review the authors give a generalized and improved version of [\textit{K. Kurdyka} and \textit{W. Pawłucki}, Stud. Math. 124, No. 3, 269--280 (1997; Zbl 0955.32006)]. The main result is the following:NEWLINENEWLINEGiven an o-minimal structure on a real closed field \(R\), let \(\Omega\) be an open definable subset of \(R^n\) and let \(E\) be a definable closed subset of \(\Omega\). Let \(p,q\) be natural numbers with \(p\leq q\) and let NEWLINE\[NEWLINEF(x,X)=\sum_{|\kappa|\leq p}\frac{1}{\kappa !}F^\kappa(x)X^\kappaNEWLINE\]NEWLINE be a definable \(C^p\)-Whitney field on \(E\) (i.e. all \(F^\kappa\)'s are definable \(C^p\)-functions). Then there exists a definable \(C^p\)-function \(f:\Omega\to R\) that is \(C^q\) on \(\Omega\setminus E\) such that \(D^\kappa f=F^\kappa\) on \(E\) for all \(\kappa\) with \(|\kappa|\leq p\).