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)).
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)
出处
《华南师范大学学报（自然科学版）》
CAS
北大核心
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)。
关键词
度量G-空间
伪等价映射
G-强链回归点
metric G-space
pseudo equivalent map
G-strong chain recurrent point
