Locally Stein Open Subsets in Normal Stein Spaces

Abstract

In this paper we present a result for the local Steinness problem: if is a locally Stein open subset of a Stein space X , does it follow that is itself Stein? We will prove that if X is normal, then for every sequence of points (x n ) n which tends to a limit x ∈ ∂ Sing(X ), there exists a holomorphic function f on which is unbounded on (x n ) n . Then, we will use this result to obtain a characterization theorem for a particular case of the Serre problem.

An interpolation property of locally Stein sets

“…This corollary improves Theorem 3.1 in [12] where h is asked only to be unbounded on the given sequence. Besides it allows us to remove the relative compactness hypothesis on D in several known results ([2, Theorems 3.3, 3.4, and 3.14]; [15, Propositions 5.5 and 5.8, and Corollary 5.16]), so for the benefit of the reader we restate them subsequently.…”