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A fixed point theorem for o-minimal structures

✍ Scribed by Kam-Chau Wong

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
113 KB
Volume
49
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

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. (Β© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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