%A 连媛, 黄小军, 李智强 %T THE PROXIMAL RELATION, REGIONALLY PROXIMAL RELATION AND BANACH PROXIMAL RELATION FOR AMENABLE GROUP ACTIONS %0 Journal Article %D 2021 %J 数学物理学报(英文版) %R 10.1007/s10473-021-0307-x %P 729-752 %V 41 %N 3 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16394.shtml} %8 2021-06-25 %X 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.