We work over an o-minimal expansion of a real closed field R. Given a closed simplicial complex K and a finite number of definable subsets of its realization |K| in R we prove that there exists a triangulation (K',f) of |K| compatible with the definable subsets such that K' is a subdivision of K and f is definably homotopic to the identity on |K|.
On O-Minimal Expansions of $(\mathbb{Q},<,+,0)$
Almost o-minimal structures and $\mathfrak X$-structures
Groups definable in o-minimal structures: various properties and a diagram
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