Bierstone, E.; Milman, P. D. Relations among analytic functions. II. (English) Zbl 0611.32003 Ann. Inst. Fourier 37, No. 2, 49-77 (1987). This is a sequel to part I of this paper (see the review above). We reduce to semicontinuity of local invariants the problem of finding \(C^{\infty}\) solutions to systems of equations involving division and composition by analytic functions. We prove semicontinuity in several general cases: in the algebraic category, for ”regular” mappings, and for module homomorphisms over a finite mapping. Cited in 4 ReviewsCited in 11 Documents MSC: 32B05 Analytic algebras and generalizations, preparation theorems 32B20 Semi-analytic sets, subanalytic sets, and generalizations Keywords:division and composition by analytic functions; semicontinuity Citations:Zbl 0611.32002 PDFBibTeX XMLCite \textit{E. Bierstone} and \textit{P. D. Milman}, Ann. Inst. Fourier 37, No. 2, 49--77 (1987; Zbl 0611.32003) Full Text: DOI Numdam EuDML