Uniform perfectness for quasi-metric spaces
Qingshan Zhou, Yaxiang Li, Ailing Xiao
TL;DR
This paper explores the conditions under which quasi-metric spaces are uniformly perfect, examines their invariance under quasim"obius maps, and presents two applications of these results.
Contribution
It establishes equivalence conditions for uniform perfectness in quasi-metric spaces and shows its invariance under quasim"obius maps, with practical applications.
Findings
Characterization of uniform perfectness in quasi-metric spaces
Invariance of uniform perfectness under quasim"obius maps
Two applications demonstrating the theory's utility
Abstract
The aim of this paper is to investigate the equivalence conditions for uniform perfectness of quasi-metric spaces. We also obtain the invariant property of uniform perfectness under quasim\"obius maps in quasi-metric spaces. In the end, two applications are given.
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Taxonomy
TopicsFixed Point Theorems Analysis · Advanced Harmonic Analysis Research · Geometric Analysis and Curvature Flows