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 
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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. http://geodesic.mathdoc.fr/articles/10.4171/jems/369/

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