Problème de Levi et espaces holomorphiquement séparés. (The Levi problem and spaces holomorphically separable) (Q1071903)

The following theorem is the main result of the paper. Let X and \(\Omega\) be analytic spaces and let \(\Pi: X\to \Omega\) be an analytic morphism with Stein fibers. If \(\Omega\) is holomorphically separable, dim X\(=n<\infty\) and the cohomology groups \(H^ p(X,{\mathcal O}_ X)\) regarded as complex vector spaces are countably dimensional (1\(\leq p\leq n-1)\) then X is a Stein space. See also the author's paper in Math. Ann. 256, 37-42 (1981; Zbl 0491.32012).