ON SINGULAR BOUNDARY POINTS OF COMPLEX FUNCTIONS

Let f be a complex valued function from the open upper halfplane E of the complex plane. We study the set of all z is an element of partial derivative E such that there exist two Stoltz angles V-1, V-2 in E wit h vertices in z (i.e., V-i is a closed angle with vertex at z and V-i\ {z}E, i=1, 2) such that the function f has different cluster sets with respect to these angles at z. E. P. Dolzhenko showed that this set of singular points is G(delta sigma) and sigma-porous for every f. He po sed the question of whether each G(delta sigma) sigma-porous set is a set of such singular points for some f. We answer this question negati vely. Namely, we construct a G(delta) porous set, which is a set of su ch singular points for no function f.