A PROBLEM ON ORDINARY FINE TOPOLOGY AND NORMAL FUNCTION

Abstract

Earlier in 1961, Doob proved that if f(z) is a normal function in a disk, then every angular cluster value at a boundary point is also a fine cluster value at the point. He then asked whether or not the converse of this theorem is true. In this paper, we answer this question in the negative sense with respect to the ordinary fine topology of Brelot.