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Uniqueness, continuity and the existence of implicit functions in constructive analysis

Published online by Cambridge University Press:  01 June 2011

H. Diener
Universitat Siegen, Fachbereich 6: Mathematik Walter-Flex-Str. 3 57072 Siegen, Germany (email:
P. Schuster
Pure Mathematics, University of Leeds, LS2 9JT, U.K. (email:


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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.

Research Article
Copyright © London Mathematical Society 2011


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