Firstly the idea of classical density topology is introduced. The properties of this topology are discussed in the aspect of separation axioms and the family of continuous functions. The first step of generalization is consideration density topology with respect to a fix sequence of positive reals tending to infinity. At this moment the idea of category aspect of the density topology is mentioned either. An approach of the density topologies with respect to the extension of Lebesgue measure is contained in the presentation. The last part concerns density topologies with respect to the sequences tending to zero. The results in this approach are relatively