Semi-monotone sets

2010/04/28 by Saugata Basu, Basu, Saugata, Andrei Gabrielov +3 · 1 citation
Computer Science · Mathematics · #Optimization and Variational Analysis #math.AG #math.GT #math.LO

paper · pdf · doi:10.48550/arxiv.1004.5047

21 page, 1 figure

arxiv created 2011/07/19 · arxiv updated 2011/07/20

Abstract

A coordinate cone in Rⁿ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of Rⁿ such that its intersection with any translation of any coordinate cone is connected. This can be viewed as a generalization of the convexity property. 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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• Monotone functions and maps

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