A Method to Estimate the Degree of $\mathbf{C}^{\mathbf{0}}$-Sufficiency of Analytic Functions

Abstract

In this paper we develop a method for an estimation of the degree of $C^0$-sufficiency of an analytic function germ $f:(\C^n,0)\to (\C,0)$. The difference between the estimation we give and the degree of $C^0$-sufficiency of $f$ will be $\leq 1$, by virtue of the results of Chang-Lu and Bochnak-Kucharz.