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Topological Groups of Lipschitz Functions and Graev Metrics

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URI: http://hdl.handle.net/2183/29916
DOI: 10.1016/j.jmaa.2021.125882

Publication date

2022

Authors

Chasco, MJ
Tkachenko, Mikhail

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Bibliographic citation

Chasco, M. J., Domínguez, X., & Tkachenko, M. G. (2022). Topological groups of Lipschitz functions and Graev metrics. Journal of Mathematical Analysis and Applications, 508(1), 125882.

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Academic degree

Abstract

[Abstract] We study the properties of the free abelian topological group Ad(X) on a metric space (X,d) endowed with the topology generated by the Graev extension dˆ of a given metric d on X. We find that the group of Lipschitz functions Lip0(X,T) is the group of continuous characters of Ad(X). From this fact we derive some interesting properties of the metric groups Ad(X) and Lip0(X,T).

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Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG

Keywords

Metric space Graev extension of metrics Lipschitz function Lipschitz free group Lipschitz group of functions Pontryagin duality

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https://doi.org/10.1016/j.jmaa.2021.125882

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Atribución 4.0 internacional

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Atribución 4.0 internacional

Except where otherwise noted, this item's license is described as Atribución 4.0 internacional