Semi-monotone sets
Logic
2011-07-20 v2 Algebraic Geometry
Geometric Topology
Abstract
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.
Cite
@article{arxiv.1004.5047,
title = {Semi-monotone sets},
author = {Saugata Basu and Andrei Gabrielov and Nicolai Vorobjov},
journal= {arXiv preprint arXiv:1004.5047},
year = {2011}
}
Comments
21 page, 1 figure