Geodesic
Semi-monotone sets
Journal of the European Mathematical Society, Tome 15 (2013) no. 2, pp. 635-657

Voir la notice de l'article provenant de la source EMS Press

A coordinate cone in Rn is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of Rn, 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.
DOI : 10.4171/jems/369
Classification : 14-XX, 57-XX, 00-XX
Keywords: o-minimal geometry, regular cell 
@article{JEMS_2013_15_2_a6,
     author = {Saugata Basu and Andrei Gabrielov and Nicolai Vorobjov},
     title = {Semi-monotone sets},
     journal = {Journal of the European Mathematical Society},
     pages = {635--657},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     doi = {10.4171/jems/369},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/369/}
}
TY  - JOUR
AU  - Saugata Basu
AU  - Andrei Gabrielov
AU  - Nicolai Vorobjov
TI  - Semi-monotone sets
JO  - Journal of the European Mathematical Society
PY  - 2013
SP  - 635
EP  - 657
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/369/
DO  - 10.4171/jems/369
ID  - JEMS_2013_15_2_a6
ER  - 
%0 Journal Article
%A Saugata Basu
%A Andrei Gabrielov
%A Nicolai Vorobjov
%T Semi-monotone sets
%J Journal of the European Mathematical Society
%D 2013
%P 635-657
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/369/
%R 10.4171/jems/369
%F JEMS_2013_15_2_a6
Saugata Basu; Andrei Gabrielov; Nicolai Vorobjov. Semi-monotone sets. Journal of the European Mathematical Society, Tome 15 (2013) no. 2, pp. 635-657. doi: 10.4171/jems/369

Cité par Sources :