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 with 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 posed 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 negatively. Namely, we construct a G(delta) porous set, which is a set of such singular points for no function f.