Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis

We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit functions theorem. This leads not only to an a priori proof of continuity, but also to an alternative, fully constructive existence proof

Problems, solutions, and completions

AbstractIf a continuous function on a complete metric space has approximate roots and in a uniform manner at most one root, then it actually has a root. We validate this heuristic principle in Bishop-style constructive mathematics without countable choice, and thus can shed some more light on the role played by the completion when it comes to solving equations