An increasing sequence of stein manifolds whose limit is not Stein
Copyright policy )An increasing sequence of stein manifolds whose limit is not Stein
This question was raised in 1933 by Behnke-Thullen [2] in the case when M is an open subset of complex Euclidean space. In the same paper they solved this problem for various special domains M. The problem was solved affirmatively for arbitrary open subsets M in IF" by Behnke-Stein [1, 1938]. K. Stein [4, 1956] proved that M is Stein if each M i is relatively Runge in Mi+ 1. Docquier-Grauert [3, 1960] showed that M is a Stein manifold if there exists a family {Mt},t~[O, 1), of Stein open subsets such that M = U M t and such O ' o_-
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510.mathematics, Stein spaces, Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs, Article, Polynomial convexity, rational convexity, meromorphic convexity in several complex variables
510.mathematics, Stein spaces, Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs, Article, Polynomial convexity, rational convexity, meromorphic convexity in several complex variables
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