A remark on ${\mathcal{C}}^{\infty }$ definable equivalence

Anna Valette, Guillaume Valette

We establish that if a submanifold $M$ of ${\mathbb{R}}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset {\mathbb{R}}^n$ which is $\mathscr{C}^\inft…