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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 355–361 (Mi semr923)  

Real, complex and functional analysis

Some problems of regularity of $f$-quasimetrics

A. V. Greshnovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, ul. Pirogova, 1, 630090, Novosibirsk, Russia

Abstract: 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, $f$-quasimetric, open set, interior and closure of a set, weak symmetry, separation axioms, convergence.

Funding Agency Grant Number
Siberian Branch of Russian Academy of Sciences I.1.2, проект № 0314-2016-0006


DOI: https://doi.org/10.17377/semi.2018.15.032

Full text: PDF file (154 kB)
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Bibliographic databases:

Document Type: Article
UDC: 515.124.2
MSC: 30L99, 53C23, 54D10
Received November 25, 2017, published April 6, 2018

Citation: A. V. Greshnov, “Some problems of regularity of $f$-quasimetrics”, Sib. Èlektron. Mat. Izv., 15 (2018), 355–361

Citation in format AMSBIB
\Bibitem{Gre18}
\by A.~V.~Greshnov
\paper Some problems of regularity of $f$-quasimetrics
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 355--361
\mathnet{http://mi.mathnet.ru/semr923}
\crossref{https://doi.org/10.17377/semi.2018.15.032}


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