Regularization of distance functions and separation axioms on $(q_1,q_2)$-quasimetric spaces

We get some estimates for interior of arbitrary $(q_1,q_2)$-quasimetric ball. We prove theorem of regularization of $(q_1,q_2)$-quasimetric that generalizes corresponding results of R. Alvarado and M. Mitrea. We introduce a notion of $\underline{\lim}$-weak symmetric $(q_1,q_2)$-quasimetric space and prove that every $\underline{\lim}$-weak symmetric $(q_1,q_2)$-quasimetric space satisfies $T_3$-axiom.