Point réguliers d'un sous-analytique. (Regular points of a subanalytic set) (Q1089471)

We give a new proof of Tamm's theorem stating that the regular part of a subanalytic set is subanalytic. Our proof doesn't use Hironaka's desingularization. Additionally, we show that, if U is an open bounded subset of \({\mathbb{R}}^ n\) and \(f: U\to {\mathbb{R}}\) is subanalytic at infinity, then there is an integer \(k\in {\mathbb{N}}\) such that f is analytic at \(x\in U\) if and only if f is k-times Gateaux differentiable in a neighborhood of x.