Regularization of distance functions and separation axioms on (q1; q2)-quasimetric spaces

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Abstract

We get some estimates for interior of arbitrary (q1; q2)-quasimetric ball. We prove theorem of regularization of (q1; q2)-quasimetric that generalizes corresponding results of R. Alvarado and M. Mitrea. We introduce a notion of lim-weak symmetric (q1; q2)-quasimetric space and prove that every lim-weak symmetric (q1; q2)-quasimetric space satisfies T3-axiom.

Original languageEnglish
Pages (from-to)765-773
Number of pages9
JournalSiberian Electronic Mathematical Reports
Volume14
DOIs
Publication statusPublished - 2017

Keywords

  • (q1; q2)-quasimetric
  • Distance function
  • Interior of (q1; q2)-quasimetric ball
  • Lim-weak symmetry
  • Open set
  • Regularization of a (q1; q2)-quasimetric
  • Separation axioms

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