The Fan Theorem and Positive-Valued Uniformly Continuous Functions on Compact Intervals
From NZJM
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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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Classification (MSC2000)
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