THE PROXIMAL RELATION,REGIONALLY PROXIMAL RELATION AND BANACH PROXIMAL RELATION FOR AMENABLE GROUP ACTIONS  

作　　者：Yuan LIAN Xiaojun HUANG Zhiqiang LI 连媛;黄小军;李智强(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China;Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Chongqing 401331,China)

机构地区：[1]College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China [2]Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Chongqing 401331,China

出　　处：《Acta Mathematica Scientia》2021年第3期729-752,共24页数学物理学报（B辑英文版）

基　　金：supported by NSF of China(11671057);NSF of Chongqing(cstc2020jcyj-msxm X0694);the Fundamental Research Funds for the Central Universities(2018CDQYST0023)。

摘　　要：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.

关 键 词：Proximal relation amenable group mean equicontinuity 

分 类 号：O19[理学—数学]