Uniqueness, continuity and the existence of implicit functions in constructive analysis
Hannes Diener, Peter M. Schuster · LMS Journal of Computation and Mathematics · 2011
Abstract We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit function theorem. Not only does this lead to an a priori proof of continuity, but also to an alternative, full proof of the implicit function theorem. Additionally, we investigate implicit functions as a case of the unique existence paradigm with parameters.