Metrically universal abelian groups
General Topology
2018-02-09 v4 Group Theory
Logic
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.
Keywords
Cite
@article{arxiv.1312.7683,
title = {Metrically universal abelian groups},
author = {Michal Doucha},
journal= {arXiv preprint arXiv:1312.7683},
year = {2018}
}
Comments
The last version's only change is the author's grant information. The new version contains simplified proofs and other changes based on the referee's comments