Sequential coarse structures of topological groups
Journal Title: Математичні Студії - Year 2019, Vol 51, Issue 1
Abstract
We endow a topological group (G,τ) with a coarse structure defined by the smallest group ideal Sτ on G containing all converging sequences and denote the obtained coarse group by (G,Sτ). If G is discrete, then (G,Sτ) is a finitary coarse group studding in {\it Geometric Group Theory}. The main result: if a topological abelian group (G,τ) contains a non-trivial converging sequence then {\it asdim} (G,Sτ)=∞. We study metrizability, normality and functional boundedness of sequential coarse groups and put some open questions.
Authors and Affiliations
I. Protasov
Keywords
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- EP ID EP584882
- DOI 10.15330/ms.51.1.12-18
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