Chasco, MJDomínguez, XabierTkachenko, Mikhail2022-03-082022-03-082022Chasco, 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.http://hdl.handle.net/2183/29916Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[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).engAtribución 4.0 internacionalhttp://creativecommons.org/licenses/by/4.0/Metric spaceGraev extension of metricsLipschitz functionLipschitz free groupLipschitz group of functionsPontryagin dualityjournal articleopen access10.1016/j.jmaa.2021.125882