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Free non-archimedean topological groups

Michael Megrelishvili, Menachem Shlossberg (2013)

Commentationes Mathematicae Universitatis Carolinae

We study free topological groups defined over uniform spaces in some subclasses of the class 𝐍𝐀 of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free balanced, free abelian and free Boolean 𝐍𝐀 groups are also metrizable. Graev type ultra-metrics determine the corresponding free topologies. Such results are in a striking contrast with free balanced and free abelian topological groups cases (in standard varieties). Another...

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