Geodesic
Some problems of regularity of $f$-quasimetrics
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 355-361

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We get a new proof for validity of $T_4$-axiom of separation for weak symmetric $f$-quasimetric spaces. Using this proof we get $T_4$-property for more general classes of $f$-quasimetric spaces. We construct the symmetric $(q,q)$-quasimetric space $(X,d)$ such that distance function $d(u,v)$ is continuous to each variables but $\lim\limits_{n\to\infty}(\rho(x_0,x_n)+\rho(y_0,y_n))=0\nRightarrow\lim\limits_{n\to \infty}\rho(x_n,y_n)=\rho(x_0,y_0)$.
Keywords: distance function, open set, interior and closure of a set, weak symmetry, separation axioms
Mots-clés : $f$-quasimetric, convergence. 
@article{SEMR_2018_15_a125,
     author = {A. V. Greshnov},
     title = {Some problems of regularity of $f$-quasimetrics},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {355--361},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a125/}
}
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A. V. Greshnov. Some problems of regularity of $f$-quasimetrics. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 355-361. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a125/