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Preprint Number 1036

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1036. Pantelis E. Eleftheriou
Semi-linear stars are contractible

Submission date: 25 April 2016


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

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Full text arXiv 1604.07329: pdf, ps.

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