26 citations · 42 across the 14 of their papers we have counts for
3 papers · 1 filter
Toric cubes are closed balls
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
We prove that toric cubes, which are images of under monomial maps, are the closures of graphs of monotone maps, and in particular semi-algebraically homeomorphic to clos…
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…