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

Part of: Real functions: Miscellaneous topics Proof theory and constructive mathematics

Published online by Cambridge University Press:  01 June 2011

H. Diener  and
P. Schuster
H. Diener
Affiliation:
Universitat Siegen, Fachbereich 6: Mathematik Walter-Flex-Str. 3 57072 Siegen, Germany (email: diener@math.uni-siegen.de)
P. Schuster
Affiliation:
Pure Mathematics, University of Leeds, LS2 9JT, U.K. (email: pschust@maths.leeds.ac.uk)

Abstract

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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.

MSC classification

Secondary: 03F60: Constructive and recursive analysis 26E40: Constructive real analysis 03F55: Intuitionistic mathematics

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 127 - 136
Copyright
Copyright © London Mathematical Society 2011

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