Metrically universal abelian groups

Michal Doucha

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arXiv · 1312.7683

Metrically universal abelian groups

Michal Doucha

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Abstract

We give a positive answer to the question of Shkarin (\emph{On universal abelian topological groups}, Mat. Sb. 190 (1999), no. 7, 127-144) whether there exists a metrically universal abelian separable group equipped with invariant metric. Our construction also gives an example of a group structure on the Urysohn universal space that is substantially different from the previously known examples. Under some cardinal arithmetic assumptions, our results generalize to higher cardinalities.

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Michal Doucha. 2013-12-30. Metrically universal abelian groups. https://arxiv.org/abs/1312.7683

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