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 |
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| Format: | Artikel |
| Sprache: | Englisch |
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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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725356833734656 |
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| author | Hernández, S. Protasov, I.V. |
| author_facet | Hernández, S. Protasov, I.V. |
| citation_txt | Balleans of topological groups / S. Hernández, I. V. Protasov // Український математичний вісник. — 2011. — Т. 8, № 1. — С. 87-100. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | 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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| first_indexed | 2025-12-07T18:52:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124412 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T18:52:18Z |
| publishDate | 2011 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Hernández, S. Protasov, I.V. 2017-09-25T18:30:40Z 2017-09-25T18:30:40Z 2011 Balleans of topological groups / S. Hernández, I. V. Protasov // Український математичний вісник. — 2011. — Т. 8, № 1. — С. 87-100. — Бібліогр.: 13 назв. — англ. 1810-3200 2010 MSC. 22A05, 22A10, 54E15, 54A25, 54D35. https://nasplib.isofts.kiev.ua/handle/123456789/124412 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. en Інститут прикладної математики і механіки НАН України Український математичний вісник Balleans of topological groups Article published earlier |
| spellingShingle | Balleans of topological groups Hernández, S. Protasov, I.V. |
| title | Balleans of topological groups |
| title_full | Balleans of topological groups |
| title_fullStr | Balleans of topological groups |
| title_full_unstemmed | Balleans of topological groups |
| title_short | Balleans of topological groups |
| title_sort | balleans of topological groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124412 |
| work_keys_str_mv | AT hernandezs balleansoftopologicalgroups AT protasoviv balleansoftopologicalgroups |