半度量空间中Bi-Lipschitz等价度量的存在性

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

Andrea Orazio Caruso, Vincenzo Palmisano

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引用次数: 0

摘要

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

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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