Polynomial criteria for the \(v\)-sufficiency of jets in classes of finitely smooth mappings
Let \(f: \mathbb R^n \rightarrow \mathbb R^m,\) \(n\geq m,\) be a \(C^{k}\)-smooth mapping, and let \(f^{r},\) \(r\leq k,\) be its \(r\)-truncation. The author studies conditions under which the solution sets of two systems of non-linear equations \(f(x)=0\) and \(f^{r}(x)=0\) are locally topologically equivalent. His idea is to formulate such conditions in terms of sufficiency problem for jets of mappings which was considered earlier in a similar context by Kuo, Kuiper, and others [\textit{T. C. Kuo}, Topology 8, 167--171 (1969; Zbl 0183.04601); Topology 11, 115--131 (1972; Zbl 0234.58005)].
scientific article; zbMATH DE number 5816872