Semi-monotone sets

Basu, Saugata, Gabrielov, Andrei, and Vorobjov, Nicolai. "Semi-monotone sets." Journal of the European Mathematical Society 015.2 (2013): 635-657. <http://eudml.org/doc/277521>.

@article{Basu2013,
abstract = {A coordinate cone in $\mathbb \{R\}^n$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $\mathbb \{R\}^n$, definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. 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.},
author = {Basu, Saugata, Gabrielov, Andrei, Vorobjov, Nicolai},
journal = {Journal of the European Mathematical Society},
keywords = {o-minimal geometry; regular cell; semialgebraic set; definable set; PL topology; triangulation; o-minimal geometry; semialgebraic set; regular cell; definable set; PL topology; triangulation},
language = {eng},
number = {2},
pages = {635-657},
publisher = {European Mathematical Society Publishing House},
title = {Semi-monotone sets},
url = {http://eudml.org/doc/277521},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Basu, Saugata
AU - Gabrielov, Andrei
AU - Vorobjov, Nicolai
TI - Semi-monotone sets
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 2
SP - 635
EP - 657
AB - A coordinate cone in $\mathbb {R}^n$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $\mathbb {R}^n$, definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. 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.
LA - eng
KW - o-minimal geometry; regular cell; semialgebraic set; definable set; PL topology; triangulation; o-minimal geometry; semialgebraic set; regular cell; definable set; PL topology; triangulation
UR - http://eudml.org/doc/277521
ER -