On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces-Reference-Cited by-同舟云学术

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

Published:2023-10-01 Issue:5 Volume:73 Page:1261-1274
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Caruso Andrea Orazio¹,Palmisano Vincenzo²

Affiliation:

1. * Dipartimento di Matematica e Informatica, Università di Catania , Viale A. Doria 6 , Catania , ITALY

2. ** Dipartimento di Matematica e Informatica, Università di Palermo , Via Archirafi 34 , Palermo , ITALY

Abstract

ABSTRACTWe 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0093/pdf

Reference27 articles.

1. Aimar, H.—Iaffei, B.—Nitti, L.: On the Macías-Segovia metrization of quasi-metric spaces, Rev. Un. Mat. Argentina 41 (1998), 67–76.

2. Assouad, P.: Plongements Lipschitziens dans ℝn , Bull. Soc. Math. France 11 (1983), 429–448.

3. Blumenthal, L. M.: Theory and Applications of Distance Geometry, Chelsea Publishing Company, 2nd ed., 1970.

4. Chittenden, E.: On the metrization problem and related problems in the theory of abstract sets, Bull. Amer. Math. Soc. 33 (1927), 13–34.

5. Chrzaszcz, K.—Jachymski, J.—Turoboś, F.: On characterizations and topology of regular semimetric spaces, Publ. Math. Debrecen 93 (2018), 87–105.