The Fan Theorem and Positive-Valued Uniformly Continuous Functions on Compact Intervals

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New Zealand Journal of Mathematics

Vol. 38, (2008), Pages 129-135


J. Berger

Department of Mathematics & Statistics

University of Canterbury

Private Bag 4800

Christchurch

New Zealand

D. Bridges

Department of Mathematics & Statistics

University of Canterbury

Private Bag 4800

Christchurch

New Zealand

mailto:d.bridges@math.canterbury.ac.nz




Abstract Julian and Richman showed that the statement "every uniformly continuous, positive-valued function on [0,1] has a positive infimum" is constructively equivalent to Brouwer's fan theorem for detachable bars. In this note we give an alternative proof of their result, a proof based on an idea of Aberth in recursive function theory.

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