Regularization of distance functions and separation axioms on (q1; q2)-quasimetric spaces

We get some estimates for interior of arbitrary (q1; q2)-quasimetric ball. We prove theorem of regularization of (q1; q2)-quasimetric that generalizes corresponding results of R. Alvarado and M. Mitrea. We introduce a notion of lim-weak symmetric (q1; q2)-quasimetric space and prove that every lim-weak symmetric (q1; q2)-quasimetric space satisfies T₃-axiom.