  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 $M=g^{-1}(0)$.
