Asymptotic dimension and small subsets in locally compact topological groups

被引：1

作者：

Banakh, Taras ^{[1
,2
]}

Chervak, Ostap ^{[2
]}

Lyaskovska, Nadya ^{[2
]}

机构：

[1] Jan Kochanowski Univ, Kielce, Poland

[2] Ivan Franko Natl Univ Lviv, Lvov, Ukraine

来源：

GEOMETRIAE DEDICATA | 2014年 / 169卷 / 01期

关键词：

Asymptotic dimension; Locally compact group; Coarse structure; Small set;

D O I：

10.1007/s10711-013-9862-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for a coarse space the ideal of small subsets of coincides with the ideal provided that is coarsely equivalent to a Euclidean space . Also we prove that for a locally compact Abelian group , the equality holds if and only if the group is compactly generated.

引用

页码：383 / 396

页数：14

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