The Fan Theorem and Unique Existence of Maxima

Journal of Symbolic Logic 71 (2):713 - 720 (2006)
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
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A. S. Troelstra (1974). Note on the Fan Theorem. Journal of Symbolic Logic 39 (3):584-596.
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