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Semi-monotone sets

Saugata Basu; Andrei Gabrielov; Nicolai Vorobjov — 2013

Journal of the European Mathematical Society

A coordinate cone in $ℝ^{n}$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $ℝ^{n}$ , 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...

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