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The Fan Theorem and Unique Existence of Maxima
Journal of Symbolic Logic 71 (2):713 - 720 (2006)
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 theoremAuthor's Profile
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Citations of this work
Brouwer's fan theorem and unique existence in constructive analysis.Josef Berger & Hajime Ishihara - 2005 - Mathematical Logic Quarterly 51 (4):360-364.
Toward a Clarity of the Extreme Value Theorem.Karin U. Katz, Mikhail G. Katz & Taras Kudryk - 2014 - Logica Universalis 8 (2):193-214.
Convexity and unique minimum points.Josef Berger & Gregor Svindland - 2019 - Archive for Mathematical Logic 58 (1-2):27-34.
Constructive Solutions of Ordinary Differential Equations.Douglas S. Bridges - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger, Logic, Construction, Computation. Berlin, Boston: De Gruyter. pp. 67-78.
References found in this work
Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation.Ulrich Kohlenbach - 1993 - Annals of Pure and Applied Logic 64 (1):27-94.
Constructing local optima on a compact interval.Douglas S. Bridges - 2007 - Archive for Mathematical Logic 46 (2):149-154.
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