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The Proximal Relation, Regionally Proximal Relation and Banach Proximal Relation for Amenable Group Actions
Acta Mathematica Scientia ( IF 1.2 ) Pub Date : 2021-04-19 , DOI: 10.1007/s10473-021-0307-x Yuan Lian , Xiaojun Huang , Zhiqiang Li
中文翻译:
适合团体行动的近邻关系,区域近邻关系和Banach近邻关系
更新日期:2021-04-19
Acta Mathematica Scientia ( IF 1.2 ) Pub Date : 2021-04-19 , DOI: 10.1007/s10473-021-0307-x Yuan Lian , Xiaojun Huang , Zhiqiang Li
In this paper, we study the proximal relation, regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions. A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation, and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.
中文翻译:
适合团体行动的近邻关系,区域近邻关系和Banach近邻关系
在本文中,我们研究了适合于群体行为的拓扑动力学系统的近邻关系,区域近邻关系和Banach近邻关系。一个有用的工具是拓扑动力学系统的支持,该拓扑动力学系统用于研究Banach近端关系的结构,并且我们证明上述三个关系都在由适当的群体作用产生的Banach平均等连续系统上重合。