Mathematical Logic Quarterly 49 (6):598 (2003)

We prove a definable analogue to Brouwer's Fixed Point Theorem for o-minimal structures of real closed field expansions: A continuous definable function mapping from the unit simplex into itself admits a fixed point, even though the underlying space is not necessarily topologically complete. Our proof is direct and elementary; it uses a triangulation technique for o-minimal functions, with an application of Sperner's Lemma
Keywords triangulation  o‐minimal structure  Fixed point  o‐minimal definability
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DOI 10.1002/malq.200310065
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