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Definability and nondefinability results for certain o-minimal structures

✍ Scribed by Hassan Sfouli

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 111 KB
Volume: 56
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200910105

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## 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 comp