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Approximation of sets defined by polynomials with holomorphic coefficients

100%

Bilski M.

Annales Polonici Mathematici

2012

tom 105

nr 2

199-207

Let X be an analytic set defined by polynomials whose coefficients $a₁,...,a_s$ are holomorphic functions. We formulate conditions on sequences ${a_{1,ν}},...,{a_{s,ν}}$ of holomorphic functions converging locally uniformly to $a₁,...,a_s$, respectively, such that the sequence ${X_{ν}}$ of sets obtained by replacing $a_j$'s by $a_{j,ν}$'s in the polynomials converges to X.

Algebraic approximation of analytic sets definable in an o-minimal structure

63%

Bilski M., Rusek K.

Annales Polonici Mathematici

2010

tom 97

nr 2

185-200

Let K,R be an algebraically closed field (of characteristic zero) and a real closed field respectively with K=R(√(-1)). We show that every K-analytic set definable in an o-minimal expansion of R can be locally approximated by a sequence of K-Nash sets.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Bilski M.

1 Rusek K.

1 2012

1 2010

Wyniki wyszukiwania

Approximation of sets defined by polynomials with holomorphic coefficients

Algebraic approximation of analytic sets definable in an o-minimal structure