Mistake in the paper ``The generalization of Whitney's lemma and application'' (Q2721552)

Consider a sequence of \(C^\infty\) functions \(x\mapsto f_m(x)\) on \(\mathbb{R}^n\). A standard adaptation of Mirkil's well-known proof of the Borel extension theorem yields a \(C^\infty\) function \((x,t)\mapsto f(x,t)\) on \(\mathbb{R}^n \times\mathbb{R}\) satisfying \(\partial^mf/ \partial t^m(x,0)= f_m(x)\) for any \(x\in \mathbb{R}^n\) and any integer \(m\geq 0\).NEWLINENEWLINENEWLINEThe author states that a mistake occurs in the writing of this argument in a paper by \textit{Yanbin Cen} and \textit{Yanming Cen} [J. Math. Res. Expo. 17, No. 3, 319-326 (1997; Zbl 0916.58004)], and he claims that Mirkil's method can not work in this setting. His claim is false, partly because he does not consider a correct notion of convergence in \(C^\infty (\mathbb{R}^n\times \mathbb{R})\). The paper is quite unclear and several other statements about function germs are not consistent.