\({\mathfrak J}\)-density points of plane sets (Q1820258)

The paper deals with the category analogue of the density topology on the plane. Similarly as for metric density, the notions of simple and strong category density points are introduced. Among others it is proved that a real function, which is continuous with respect to this topology, is Darboux Baire one. Also the coarsest topology for the class of continuous functions is described. Similar results for one-dimensional category density topology can be found in \textit{W. Poreda, E. Wagner-Bojakowska} and \textit{W. Wilczyński} [Fundam. Math. 125, 167-173 (1985; Zbl 0613.26002)].