TY - JOUR

T1 - Symmetrizations of Distance Functions and f-Quasimetric Spaces

AU - Greshnov, A. V.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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)}.

AB - 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)}.

KW - (q, q)-quasimetric

KW - distance function

KW - extreme point

KW - f-quasimetric

KW - symmetrization

UR - http://www.scopus.com/inward/record.url?scp=85071469878&partnerID=8YFLogxK

U2 - 10.3103/S1055134419030052

DO - 10.3103/S1055134419030052

M3 - Article

AN - SCOPUS:85071469878

VL - 29

SP - 202

EP - 209

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 3

ER -