Abstract
We prove theorems on the topological equivalence of distance functions on spaces with weak and reverse weak symmetries. We study the topology induced by a distance function ρ under the condition of the existence of a lower symmetrization for ρ by an f-quasimetric. For (q1, q2)-metric spaces (X, ρ), we also study the properties of their symmetrizations min {ρ(x, y), ρ(y, x)} and max {ρ(x, y), ρ(y, x)}. The relationship between the extreme points of a (q1q2)-quasimetric ρ and its symmetrizations min{ρ(x, y), ρ(y, x)} and max {ρ(x, y), ρ(y, x)}.
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Acknowledgments
The author expresses his deep gratitude to the referee for evincing interest in his work.
Funding
The work was supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant 1.1.2; Project 0314-2016-0006).
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Russian Text © The Author(s), 2018, published in Matematicheskie Trudy, 2018, Vol. 21, No. 2, pp. 150–162.
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Greshnov, A.V. Symmetrizations of Distance Functions and f-Quasimetric Spaces. Sib. Adv. Math. 29, 202–209 (2019). https://doi.org/10.3103/S1055134419030052
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DOI: https://doi.org/10.3103/S1055134419030052