Balleans of topological groups
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Balleans of topological groupsDate
2011Publisher
Springer VerlagISSN
0041-5995; 1573-9376Bibliographic citation
Ukrainian Mathematical Journal (2011) vol. 8, no. 1, p.86-99Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/sumittedVersionSubject
Abstract
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 ... [+]
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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