Some modifications of density topologies (Q2747070)

The paper introduces two topologies in the plane, banking on the notions of density and \(I\)-density. The concept of a regular density point is utilized for the introduction of the topologies. It is shown that the first introduced topology is essentially stronger than the Euclidean topology and essentially weaker than the density topology on the plane. For the other, it is seen to be essentially stronger than the Euclidean topology and essentially weaker than the \(I\)-density topology, on the plane. Separation axioms with respect to the two topologies are investigated and functions continuous with respect to these topologies are studied as well.