AN EXAMPLE IN TANGENTIAL MEROMORPHIC APPROXIMATION

It is known that all sets of meromorphic uniform approximation in C wh ich satisfy an additional condition involving the Gleason parts of the algebra R(K) are then also sets of tangential approximation by meromo rphic functions. In this paper, we construct a set which, although it is a set of tangential approximation, does not satisfy this extra cond ition on parts and, thus, showing that the condition fails to be neces sary. Finding a complete characterization of sets of meromorphic tange ntial approximation is still an open problem. (C) 1996 Academic Press, Inc.