Strict $${\mathcal {C}}^p$$-triangulations of sets locally definable in o-minimal structures with an application to a $$\mathcal C^p$$-approximation problem

Abstract

We show how to derive triangulations of sets locally definable in o-minimal structures from triangulations of compact definable sets. We give it in particular for strict $$\mathcal C^p$$ C p -triangulations which has been recently studied by the author. This combined with a theorem of Fernando and Ghiloni implies that every continuous mapping defined on a locally compact subset B of $$\mathbb R^m$$ R m with values in any locally definable and locally compact subset A of $$\mathbb R^n$$ R n can be approximated by $$\mathcal C^p$$ C p -mappings defined on B with values in A for any positive integer p.