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The fan theorem and unique existence of maxima

Published online by Cambridge University Press:  12 March 2014

Josef Berger
Affiliation:
Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany. E-mail: josef.berger@mathematik.uni-muenchen.de
Douglas Bridges
Affiliation:
Department of Mathematics & Statistics, The University of Canterbury, Private Bag 4800, Christchurch, New Zealand. E-mail: D.Bridges@math.canterbury.ac.nz
Peter Schuster
Affiliation:
Mathematisches Institut der Universität Münchenm, Theresienstr. 39, 80333 München, Germany. E-mail: peter.schuster@mathematik.uni-muenchen.de

Abstract

The existence and uniqueness of a maximum point for a continuous real–valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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