%0 Journal Article
%T On Graev type ultra-metrics
%A Menachem Shlossberg
%J Mathematics
%D 2014
%I arXiv
%X We study Graev ultra-metrics which were introduced by Gao. We show that the free non-archimedean balanced topological group defined over an ultra-metric space is metrizable by a Graev ultra-metric. We prove that the Graev ultra-metric has a maximal property. Using this property, among others, we show that the Graev ultra-metric associated with an ultra-metric space $(X,d)$ with diameter$\leq 1$ coincides with the ultra-metric $\hat{d}$ of Savchenko and Zarichnyi.
%U http://arxiv.org/abs/1405.2244v1