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Preprint Number 1036
1036. Pantelis E. Eleftheriou Semi-linear stars are contractible E-mail: Submission date: 25 April 2016 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 from [5]. 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. Mathematics Subject Classification: 03C64 Keywords and phrases: |

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