Density topology
by
Władysław Wilczyński
University of Lodz, Poland

The papers of Goffman, Neugebauer, Nishiura (1961) and Goffman, Waterman (1961) were the starting point for systematic study of the density topology in Euclidean spaces. However, the notions of a density point and an approximately continuous functions were considered much earlier by Lebesgue (1904) and Denjoy (1916) and the density topology was defined by Haupt and Pauc in 1952 in a paper which had almost no impact. In the eighties we have studied so called I-density topology being a Baire category analogue of the density topology. In a series of papers we presented the similarities and differences between these two topologies creating, in some sense, refinement of the excellent book "Measure and category" by J. Oxtoby.

Another kind of topologies are so called \Psi-density topologies introduced in the nineties with the use of the regulator function \Psi. This notion have been inspired by the results of Taylor (1959). Also the effort have been made for the study of the category analogue of the \Psi-density topology.

Date received: July 20, 2001