An application of \(q\)-concavity to increasing sequences of Stein open sets (Q2572620)

Using a criterion for analyticity of \(q\)-concave sets, obtained by \textit{V. Vâjâitu} [Ann. Inst. Fourier Grenoble 50, No.~4, 1191--1203 (2000; Zbl 0974.32006)], the authors give an elementary proof of the proposition due to M.~Colţoiu: Let \(X\) be a normal Stein space and \(D\subset X\) a relatively compact open set which is an increasing union of Stein open sets. Then \(D\) is a domain of holomorphy. This proposition is deduced as a consequence of the following two facts: (i) For every point \(x_0\in \text{Reg}(X)\cap\partial D\) and for every sequence \(\{x_n\}\) in \(D\) converging to \(x_0\), there is a holomorphic function \(f\in\mathcal O(D)\) such that the sequence \(\{f(x_n)\}\) is unbounded. (ii) The set \(\partial D\setminus\text{Sing}(X)\) is dense in \(\partial D\). The main contribution of this article is an interesting proof of (ii) using certain facts about \(q\)-convexity with corners and the subsequent Vâjâitu criterion of analyticity.