Semilinear stars are contractible
Semilinear stars are contractible
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2018
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Fundamenta Mathematicae ; 241 (2018), 3. - pp. 291-312. - ISSN 0016-2736. - eISSN 1730-6329
Abstract
Let 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.
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510 Mathematics
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ELEFTHERIOU, Pantelis E., 2018. Semilinear stars are contractible. In: Fundamenta Mathematicae. 241(3), pp. 291-312. ISSN 0016-2736. eISSN 1730-6329. Available under: doi: 10.4064/fm394-10-2017BibTex
@article{Eleftheriou2018Semil-42664,
year={2018},
doi={10.4064/fm394-10-2017},
title={Semilinear stars are contractible},
number={3},
volume={241},
issn={0016-2736},
journal={Fundamenta Mathematicae},
pages={291--312},
author={Eleftheriou, Pantelis E.}
}
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