Semi-linear stars are contractible
Logic
2019-10-02 v2
Abstract
Let be an ordered vector space over an ordered division ring. We prove that every definable set 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 is definably simply-connected. In fact, if the star is bounded, then it is definably contractible.
Cite
@article{arxiv.1604.07329,
title = {Semi-linear stars are contractible},
author = {Pantelis E. Eleftheriou},
journal= {arXiv preprint arXiv:1604.07329},
year = {2019}
}