A numerical approach to some basic theorems in singularity theory

摘要

In this paper, we give the explicit bounds for the data of objects involvedin some basic theorems of Singularity theory: the Inverse, Implicit and RankTheorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the densityand openness of Morse functions. We expect that the results will makeSingularities more applicable and will be useful for Numerical Analysis andsome fields of computing.