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

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. © 2017 Elsevier B.V.

Authors
Arutyunov A.V. 1, 2 , Greshnov A.V. 3, 4 , Lokutsievskii L.V. 2, 5 , Storozhuk K.V. 3, 4
Journal
Topology and its Applications
Language
English
Pages
178-194
State
Published
Link
External link
DOI
10.1016/J.TOPOL.2017.02.035
Volume
221
Year
2017
Organizations
  • 1 RUDN University, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
  • 2 Lomonosov Moscow State University, MSU, Leninskiye Gory, Moscow, 119991, Russian Federation
  • 3 Novosibirsk State University, Pirogova str. 1, Novosibirsk, 630090, Russian Federation
  • 4 Sobolev Institute of Mathematics, pr. Koptyuga 4, Novosibirsk, 630090, Russian Federation
  • 5 Steklov Mathematical Institute of Russian Academy of Sciences, Russian Federation
Keywords
f-Quasimetric space; Metrizability; Quasimetric
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