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Vietnam Journal of Mathematics 35:2(2007) 187-199  The Degree of $C^0$-sufficiency of Analytic Function Germs With Respect to an Ideal Pham Tien Son Abstract.  Let $f \colon ({\Bbb C}^2, 0) \rightarrow ({\Bbb C}, 0)$ be an analytic function germ of two complex variables and let $I$ be an ideal of ${\Bbb C}\{x, y\}.$ We give some formulae for the degree of $C^0$-sufficiency of $f$ with respect to $I.$ When $I$ is the maximal ideal we retrieve a result of T.~ C. ~Kuo and Y. ~C. ~Lu.   2000 Mathematics Subject Classification: 32C40, 58K40; Secondary: 14H20, 32S05. Keywords: $C^0$-sufficiency, Equisingularity, $\mu$-constant, Newton polygon.

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