On strong essential cluster sets (Q789558)

The author considers the boundary behaviour of a function defined in the upper half plane and assuming values in a second countable topological space. The main result of the paper is the following theorem: for each such function the set of directional limit points at the direction \(\pi\) /2 is included in the set of strong essential limit points for almost every x. Moreover if a function is Baire 1, then the exceptional set is also of the first category.