On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2023-10-01 DOI:10.1515/ms-2023-0093

Andrea Orazio Caruso, Vincenzo Palmisano

引用次数: 0

Abstract

ABSTRACT We provide an overview of the known problem on the existence of a bi-Lipschitz equivalent metric with respect to a given quasi-ultrametric, revisiting known results and counterexamples in an unified approach based on the existence of a relaxed polygonal inequality. We present new proofs and characterizations of classical results using different techniques.

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半度量空间中Bi-Lipschitz等价度量的存在性

摘要:我们概述了关于给定准超度量的双lipschitz等效度量的存在性的已知问题，并基于松弛多边形不等式的存在性以统一的方法重审了已知结果和反例。我们提出了新的证明和表征经典结果使用不同的技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.