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Semilinear stars are contractible

Volume 241 / 2018

Pantelis E. Eleftheriou Fundamenta Mathematicae 241 (2018), 291-312 MSC: Primary 03C64. DOI: 10.4064/fm394-10-2017 Published online: 29 January 2018

Abstract

Let $ {\mathcal {R}}$ be an ordered vector space over an ordered division ring. We prove that every definable set $X$ is a finite union of relatively open definable subsets which are definably simply-connected, settling a conjecture of Edmundo et al. (2013). The proof goes through the stronger statement that the star of a cell in a special linear decomposition of $X$ is definably simply-connected. In fact, if the star is bounded, then it is definably contractible.

Authors

  • Pantelis E. EleftheriouDepartment of Mathematics and Statistics
    University of Konstanz
    Box 216
    78457 Konstanz, Germany
    e-mail

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