Large Discrete Sets in Stein Manifolds

Jörg Winkelmann

Abstract.

Rosay and Rudin constructed examples of discrete subsets of Cn with remarkable properties. We generalize these constructions from Cn to arbitrary Stein manifolds. We prove: Given a Stein manifold X and a affine variety V of the same dimension there exists a discrete subset D in X such that

We also give examples which demonstrate that such discrete subsets can not be found in arbitrary non-Stein manifolds.
Appeared in:
Mathematischen Zeitschrift . 236, (4), 883-901 (2001)


Related later work:
Tameness and growth conditions.
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Last modification: 31 March 2008