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can anyone give me a precise statement of the "closure of modules" theorem in several complex variables? it says something like: a criterion for the germ of a function to belong to the stalk of an ideal at a point, is that the function can be uniformly approximated on neighborhoods of that point by functions whose stalks do lie in the ideal. I have forgotten my gunning and rossi.
so it is something like, if for every e>0 there is a nbhd V of p and a function in the ideal I which is uniformly closer to f than e on V, then f belongs to I.
? And are there some bounds on the coefficients of the generators of the ideal in terms of given bounds on the coefficients of the approximating functions?
so it is something like, if for every e>0 there is a nbhd V of p and a function in the ideal I which is uniformly closer to f than e on V, then f belongs to I.
? And are there some bounds on the coefficients of the generators of the ideal in terms of given bounds on the coefficients of the approximating functions?