Triangulations of monotone families I: Two-dimensional families

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov

Let $K\subset {\mathbb{R}}^n$ be a compact definable set in an o-minimal structure over $\mathbb{R}$, e.g., a semi-algebraic or a subanalytic set. A definable family $\{ S_δ|\> 0< δ…