2016/04/25 by Eleftheriou, Pantelis E.
#03C64 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1604.07329
Let \cal 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.