Semi-monotone sets | Zendy

Saugata Basu | Zendy; Andrei Gabrielov | Zendy; Nicolai Vorobjov | Zendy

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Semi-monotone sets

Author(s) -

Saugata Basu,

Andrei Gabrielov,

Nicolai Vorobjov

Publication year - 2013

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/369

Subject(s) - mathematics , monotone polygon , pure mathematics , combinatorics , geometry

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

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