Published online by Cambridge University Press: 20 November 2018
Notation. For S a subset of the extended plane C* = C ∪ (∞ ) let S0 be its interior, its closure in C* and
its boundary. H(S) and M(S) will denote the sets of all restrictions to S of functions which are, on a neighborhood of S, holomorphic or meromorphic, respectively. A (S) will stand for the set of functions from S to C* which are continuous on S and whose restriction to S° are holomorphic.