Density topology in a topological group (Q762294)

In this paper we develop a theory of density topology in a topological group X. With the help of the density function in X we generate a topology (called density topology). We show that this topology is finer than the originnal topology of X. We further prove that X endowed with the density topology is Hausdorff, non first countable, non separable, regular and a Baire space. Defining a d-limit point suitably, we also verify that the topology generated by the closure axioms is identified with the open set topology (open with respect to the density topology).