# 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.

**Keywords**

**Classification** (MSC2000)

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