%0 Journal Article
%T Semi-monotone sets
%A Saugata Basu
%A Andrei Gabrielov
%A Nicolai Vorobjov
%J Mathematics
%D 2010
%I arXiv
%X A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of R^n such that its intersection with any translation of any coordinate cone is connected. This can be viewed as a generalization of the convexity property. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone set is a topological regular cell.
%U http://arxiv.org/abs/1004.5047v2