The group of isometries of a locally compact metric space with one end

Antonios Manoussos

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The group of isometries of a locally compact metric space with one end

机译：具有一端的局部紧凑度量空间的一组等距

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In this note we study the dynamics of the natural evaluation action of the group of isometries G of a locally compact metric space (X,d) with one end. Using the notion of pseudo-components introduced by S. Gao and A.S. Kechris we show that X has only finitely many pseudo-components exactly one of which is not compact and G acts properly on this pseudo-component. The complement of the non-compact component is a compact subset of X and G may fail to act properly on it.

机译：在此注释中，我们研究了具有一端的局部紧凑度量空间（X，d）的等距群G的自然评估作用的动力学。使用S. Gao和A.S.提出的伪成分概念Kechris我们证明X仅具有有限的许多伪分量，而其中之一并不紧凑，而G对该伪分量的作用适当。非紧凑组件的补码是X的紧凑子集，G可能无法对其正确起作用。

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来源
《Topology and its applications》 |2010年第18期|p.2876-2879|共4页
作者
Antonios Manoussos;
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作者单位

Fakultat fuer Mathematik, SFB 701, Universitaet Bielefeld. Postfach 100131, D-33501 Bielefeld, Germany;

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原文格式 PDF
正文语种 eng
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关键词
proper action; pseudo-component; freudenthal compactification; end-point compactification; ends; J-space;

机译：适当的行动;伪分量弗氏压实;端点压实;结束;空间;

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专利

1. Compact metrizable groups are isometry groups of compact metric spaces [J] . Melleray J Proceedings of the American Mathematical Society . 2008,第4期

机译：紧凑的可度量组是紧凑的度量空间的等距组
2. Mappings and isometries of compact metric spaces [J] . Iliadis Stavros Topology and its applications . 2017,第apra15期

机译：紧度量空间的映射和等距
3. Existence and examples of quantum isometry groups for a class of compact metric spaces [J] . Goswami Debashish Advances in Mathematics . 2015,第Null期

机译：一类紧凑度量空间的量子等距群的存在与示例
4. Uniformly locally compact and close to them spaces [C] . B. E. Kanetov, D. E. Kanetova, N. A. Baigazieva International Conference of Mathematical Sciences . 2021

机译：均匀地紧凑，靠近它们空间
5. Graev metrics and isometry groups of Polish ultrametric spaces. [D] . Shi, Xiaohui. 2013

机译：波兰超度量空间的Graev度量和等距组。
6. Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds [O] . Abhishek Bhattacharya, David B. Dunson -1

机译：具有特定歧管的紧凑型度量空间上的非参数贝叶斯密度估计的强稠度
7. The role of connectedness in the structure and the action of group of isometries of locally compact metric spaces [O] . Manoussos, Antonios, Strantzalos, Polychronis 2000

机译：连通性在结构和群体行为中的作用局部紧凑度量空间的等距
8. Isomorphical Classification of Function Spaces of Zero Dimensional Locally Compact Separable Metric Spaces [R] . Baars, J. , de Groot, J. A. M. 1988

机译：零维局部紧致可分度量空间函数空间的同构分类

The group of isometries of a locally compact metric space with one end

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