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：

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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。