Cluster Sets of Pseudomeromorphic Functions

Abstract

We shall restrict our attention to functions w = f{z) defined and pseudomeromorphic in |z| < 1. We make no assumptions about the unit circle \z\ = 1, on which some of the points may be regular points, poles or essential singularities.The cluster set of f(z) at 2 0 , 1201 = 1, C(f f ZQ), is the set of all points a for which there exists a sequence {z n ), U«|<1, such that Iim2 n = zo and lim/(2n) = a.