Abstract
The paper surveys available and new results relating to the implicit function problem for parametric inclusions in metric spaces. As in the metric regularity theory, the metric viewpoint allows to single out and clarify some basic principles that eventually leads to unification and simplification of techniques used in specific situations. Among the results there is a fairly complete collection of infinitesimal sufficient conditions for regularity related properties (subregularity, Lipschitz dependence etc.) and associated results on implicit functions based on uniform versions of the properties. The paper is concluded with a demonstration how the presented general results can be applied to get a simple and transparent proof of the main stability theorems for solution maps of generalized equations.
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