Topological and geometrical properties of spaces with symmetric and nonsymmetric f-quasimetrics

A. V. Arutyunov; A. V. Greshnov; L. V. Lokutsievskii; K. V. Storozhuk

doi:10.1016/j.topol.2017.02.035

Topological and geometrical properties of spaces with symmetric and nonsymmetric f-quasimetrics

A. V. Arutyunov, A. V. Greshnov, L. V. Lokutsievskii, K. V. Storozhuk

Mathematical Analysis Section

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

The properties of spaces equipped with a topology defined by a distance function are studied. The considered distance function is not necessarily symmetric but satisfies the so-called f-triangle inequality, which is a weakened version of the usual triangle inequality. Sufficient conditions for metrizability of such spaces are proposed. A construction of a quasimetric topologically equivalent to a given f-quasimetric is proposed.

Original language	English
Pages (from-to)	178-194
Number of pages	17
Journal	Topology and its Applications
Volume	221
DOIs	https://doi.org/10.1016/j.topol.2017.02.035
Publication status	Published - 15 Apr 2017

Keywords

f-Quasimetric space
Metrizability
Quasimetric

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10.1016/j.topol.2017.02.035

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abstract = "The properties of spaces equipped with a topology defined by a distance function are studied. The considered distance function is not necessarily symmetric but satisfies the so-called f-triangle inequality, which is a weakened version of the usual triangle inequality. Sufficient conditions for metrizability of such spaces are proposed. A construction of a quasimetric topologically equivalent to a given f-quasimetric is proposed.",

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AU - Lokutsievskii, L. V.

AU - Storozhuk, K. V.

PY - 2017/4/15

Y1 - 2017/4/15

N2 - The properties of spaces equipped with a topology defined by a distance function are studied. The considered distance function is not necessarily symmetric but satisfies the so-called f-triangle inequality, which is a weakened version of the usual triangle inequality. Sufficient conditions for metrizability of such spaces are proposed. A construction of a quasimetric topologically equivalent to a given f-quasimetric is proposed.

AB - The properties of spaces equipped with a topology defined by a distance function are studied. The considered distance function is not necessarily symmetric but satisfies the so-called f-triangle inequality, which is a weakened version of the usual triangle inequality. Sufficient conditions for metrizability of such spaces are proposed. A construction of a quasimetric topologically equivalent to a given f-quasimetric is proposed.

KW - f-Quasimetric space

KW - Metrizability

KW - Quasimetric

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JO - Topology and its Applications

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SN - 0166-8641

ER -

Topological and geometrical properties of spaces with symmetric and nonsymmetric f-quasimetrics

Abstract

Keywords

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