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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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2011
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| Series: | Український математичний вісник |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/124412 |
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| 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 ⊆ 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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