Topological Groups of Lipschitz Functions and Graev Metrics
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http://hdl.handle.net/2183/29916
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Topological Groups of Lipschitz Functions and Graev MetricsDate
2022Citation
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.
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).
Keywords
Metric space
Graev extension of metrics
Lipschitz function
Lipschitz free group
Lipschitz group of functions
Pontryagin duality
Graev extension of metrics
Lipschitz function
Lipschitz free group
Lipschitz group of functions
Pontryagin duality
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Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG
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Atribución 4.0 internacional
