度量G-空间中G-强链回归点集的动力学性质  

The Dynamical Property of G-Strong Chain Recurrent Point Set in Metric G-space

作　　者：冀占江 JI Zhanjiang(School of Data Science and Software Engineering/Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System/Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Wuzhou 543002, China)

机构地区：[1]梧州学院大数据与软件工程学院/广西高校图像处理与智能信息系统重点实验室/广西高校行业软件技术重点实验室,梧州543002

出　　处：《华南师范大学学报（自然科学版）》2022年第2期115-119,共5页Journal of South China Normal University(Natural Science Edition)

基　　金：广西自然科学基金项目(2020JJA110021);梧州学院校级重点项目(2020B007)。

摘　　要：在拓扑群作用下的度量空间中研究了G-强链回归点集的拓扑结构和特征,得到G-强链回归点集的若干结论:(1)设(X,d)是紧致度量G-空间,G是紧致的拓扑群,f:X→X连续,则SCR_(G)(f)是闭集;(2)设(X,d)是紧致度量G-空间,G是紧致的拓扑群,f:X→X同胚伪等价,则f(SCR_(G)(f))=SCR_(G)(f);(3)设(X,d)是紧致度量G-空间,f:X→X同胚伪等价且度量d对群G不变,则SCR_(G)(f)=SCR_(G)(f^(-1))。The topological structure and characteristics of G-strong chain regression point set are studied in the metric space under topological group action and some conclusions of G-strong chain regression point set are obtained:(1)Let(X,d)be a compact metric G-space,G be a compact topological group,and f:X→X be a continuous map;then the set SCR_(G)(f)is a closed set;(2)Let(X,d)be a compact metric G-space,G be a compact topological group,andf:X→Xbe an homeomorphic pseudoequivalent map;then f(SCR_(G)(f))=SCR_(G)(f);(3)Let(X,d)be a compact metric G-space,f:X→Xbe an homeomorphic pseudoequivalent map and the metric d be invariant to group G;then SCR_(G)(f)=SCR_(G)(f^(-1)).

关 键 词：度量G-空间 伪等价映射 G-强链回归点 

分 类 号：O189.11[理学—数学]