All plane domains are Banach-Stein

Abstract

In this short note we show, by using the $$\tfrac{1}{4}$$ -Theorem of Koebe-Bieberbach, that every domain in ℂ is Banach-Stein in the sense of G. Fischer and, as a consequence, a holomorphic fiber bundle over a Stein space whose fiber is an open subset of ℂ is Stein.