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The normality domain of a family of holomorphic functions on a Stein space. (English) Zbl 1278.32004

Summary: Let \(X\) be a Stein space. Then we prove that, for any family \(\mathcal F\subset\mathcal O(X)\), every normality domain of it in the strong sense is a \(\mathcal O(X)\)-convex domain of \(X\).

MSC:

32A19 Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.)
32E10 Stein spaces
32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
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