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.
Uniqueness, continuity and the existence of implicit functions in constructive analysis
Schuster, P.
2011-01-01
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.
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