401 citations · 727 across the 45 of their papers we have counts for
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A Helly-type theorem for semi-monotone sets and monotone maps
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
We consider sets and maps defined over an o-minimal structure over the reals, such as real semi-algebraic or subanalytic sets. A {\em monotone map} is a multi-dimensional generaliz…
Monotone functions and maps
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over…
Semi-monotone sets
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
A coordinate cone in R^n 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 rea…