Abstract
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and openness of Morse functions. We expect that the results will make Singularities more applicable and will be useful for Numerical Analysis and some fields of computing.
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