Symmetrizations of Distance Functions and f-Quasimetric Spaces

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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)}.

Original languageEnglish
Pages (from-to)202-209
Number of pages8
JournalSiberian Advances in Mathematics
Issue number3
Publication statusPublished - 1 Jul 2019


  • (q, q)-quasimetric
  • distance function
  • extreme point
  • f-quasimetric
  • symmetrization


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