Geodesic
Regularization of distance functions and separation axioms on $(q_1,q_2)$-quasimetric spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 765-773

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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.
Keywords: distance function, open set, interior of $(q_1,q_2)$-quasimetric ball, $\underline{\lim}$-weak symmetry, separation axioms, regularization of a $(q_1,q_2)$-quasimetric.
Mots-clés : $(q_1,q_2)$-quasimetric 
@article{SEMR_2017_14_a120,
     author = {A. V. Greshnov},
     title = {Regularization of distance functions and separation axioms on $(q_1,q_2)$-quasimetric spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {765--773},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a120/}
}
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A. V. Greshnov. Regularization of distance functions and separation axioms on $(q_1,q_2)$-quasimetric spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 765-773. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a120/