Journal article:
Semilinear stars are contractible

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2018
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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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Fundamenta Mathematicae ; 241 (2018), 3. - pp. 291-312. - ISSN 0016-2736. - eISSN 1730-6329
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ISO 690ELEFTHERIOU, 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/fm394-10-2017
BibTex
@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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    <dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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