Geodesic
Metric topological groups: their metric approximation and metric ultraproducts
Michal Doucha1 orcid
1Czech Academy of Sciences, Prague, Czechia, and University of Franche-Comté, Besançon, France
Groups, geometry, and dynamics, Tome 12 (2018) no. 2, pp. 615-636

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DOI

We define a metric ultraproduct of topological groups with left-invariant metric, and show that there is a countable sequence of finite groups with left-invariant metric whose metric ultraproduct contains isometrically as a subgroup every separable topological group with left-invariant metric.
DOI : 10.4171/ggd/450
Classification : 22-XX, 03-XX, 20-XX, 46-XX
Mots-clés : Metric approximation, left-invariantmetric, metric ultraproducts, sofic groups, weakly sofic groups

Michal Doucha  1

1 Czech Academy of Sciences, Prague, Czechia, and University of Franche-Comté, Besançon, France 
Michal Doucha. Metric topological groups: their metric approximation and metric ultraproducts. Groups, geometry, and dynamics, Tome 12 (2018) no. 2, pp. 615-636. doi: 10.4171/ggd/450
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     title = {Metric topological groups: their metric approximation and metric ultraproducts},
     journal = {Groups, geometry, and dynamics},
     pages = {615--636},
     year = {2018},
     volume = {12},
     number = {2},
     doi = {10.4171/ggd/450},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/450/}
}
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