Bifurcation values of $C^{\infty} functions

We show how one can use a trivialization of a function $f : \mathbb{R}^n\to\mathbb{R}$ to construct a trivialization of $f$ in $\mathbb{R}^n$. Additionally we adopt a method for trivialising functions which satisfy the $\rho_0$-regularity condition to the case of functions defined on hypersurfaces of the form $M=g^{-1}(0)$.