Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)


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.
Original languageEnglish
Pages (from-to)635-657
Number of pages23
JournalJournal of the European Mathematical Society
Issue number2
Publication statusPublished - 2013


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