On Graev type ultra-metrics

Menachem Shlossberg

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arXiv · 1405.2244

On Graev type ultra-metrics

Menachem Shlossberg

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Abstract

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.

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Menachem Shlossberg. 2014-05-09. On Graev type ultra-metrics. https://arxiv.org/abs/1405.2244

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