Local normality of a meromorphic function and a Picard type theorem (Q1081728)

The maximal ideal space M of the Banach algebral \(H^{\infty}\) of bounded holomorphic functions on the unit disc D provides an important compactification of D. A point m of M is called regular if M has a certain analytic structure at m. The author shows the following Picard type theorem. If a meromorphic function f in D is not continuously extendable to a regular point m of the ''corona'' \(M\setminus D\), then f assumes every value, except possibly two, infinitely often in every neighborhood of m. [Reviewer's remark: To what extent can D be replaced by a more general domain ?]