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:

Full text arXiv 1604.07329: pdf, ps.