# Semi-monotone sets

Saugata Basu; Andrei Gabrielov; Nicolai Vorobjov

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 2, page 635-657
- ISSN: 1435-9855

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topBasu, 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 -

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