# Approximation of sets defined by polynomials with holomorphic coefficients - Mathematics > Complex Variables

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Abstract: Let X be an analytic set defined by polynomials whose coefficientsa 1,

.,a s are holomorphic functions. We formulate conditions such that forall sequences {a 1,n},

.,{a s,n} of holomorphic functions converginglocally uniformly to a 1,

.,a s respectively the following holds true. Ifa 1,n,

.,a s,n satisfy the conditions then the sequence of the sets {X n}obtained by replacing a j by a j,n in the polynomials, converge to X.

Author: ** Marcin Bilski**

Source: https://arxiv.org/