Balleans of topological groups
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 ⊆ FU, S ⊆ UF. The family of all bounded subsets of G determines two structures on G, namely the left and right balleans Bl(G) and Br(G) , which are coun...
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| Veröffentlicht in: | Український математичний вісник |
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| Datum: | 2011 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/124412 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Balleans of topological groups / S. Hernández, I. V. Protasov // Український математичний вісник. — 2011. — Т. 8, № 1. — С. 87-100. — Бібліогр.: 13 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 ⊆ FU, S ⊆ UF. The family of all bounded subsets of G determines two structures on G, namely the left and right balleans Bl(G) and Br(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.
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| ISSN: | 1810-3200 |