An Example in Tangential Meromorphic Approximation Original Research Article

It is known that all sets of meromorphic uniform approximation inCwhich satisfy an additional condition involving the Gleason parts of the algebraR(K) are then also sets of tangential approximation by meromorphic functions. In this paper, we construct a set which, although it is a set of tangential approximation, does not satisfy this extra condition on parts and, thus, showing that the condition fails to be necessary. Finding a complete characterization of sets of meromorphic tangential approximation is still an open problem.