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Balleans of topological groups. (English. Ukrainian original) Zbl 1291.22002

J. Math. Sci., New York 178, No. 1, 65-74 (2011); translation from Ukr. Mat. Visn. 8, No. 1, 87-100 (2011).
Summary: A subset \(S\) of a topological group \(G\) is called bounded if, for every neighborhood \(U\) of the identity of \(G\), there exists a finite subset \(F\) such that \(S\subseteq FU, S\subseteq\;UF\). The family of all bounded subsets of \(G\) determines two structures on \(G,\) namely the left and right balleans \(B_l(G)\) and \(B_r(G)\), which are counterparts of the left and right uniformities of \(G\). We study the relationships between the uniform and ballean structures on \(G\), describe all topological groups admitting a metric compatible both with uniform and ballean structures, and construct a group analogue of Higson’s compactification of a proper metric space.

MSC:

22A10 Analysis on general topological groups
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References:

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