Metric topological groups: their metric approximation and metric ultraproducts

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00490729" target="_blank" >RIV/67985840:_____/18:00490729 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4171/GGD/450" target="_blank" >http://dx.doi.org/10.4171/GGD/450</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/GGD/450" target="_blank" >10.4171/GGD/450</a>

Result language
angličtina
Original language name
Metric topological groups: their metric approximation and metric ultraproducts
Original language description
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. In particular, there is a countable sequence of finite groups with left-invariant metric such that every finite subset of an arbitrary topological group with left-invariant metric may be approximated by all but finitely many of them. We compare our results with related concepts such as sofic groups, hyperlinear groups and weakly sofic groups.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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