Behnke–Stein theorem

In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence

It was proved by Heinrich Behnke and Karl Stein in 1938.

[1] This is related to the fact that an increasing union of pseudoconvex domains is pseudoconvex and so it can be proven using that fact and the solution of the Levi problem.

This theorem again holds for Stein manifolds, but it is not known if it holds for Stein space.

[2] This mathematical analysis–related article is a stub.