摘要
仿造度量空间中链回归点的定义,给出了拓扑群作用下度量空间中G-链回归点的概念,并将度量空间中链回归点的一些结论,推广到拓扑群作用下度量空间中,得到如下结果:1)同胚伪等价映射f的G-链回点集等于它的逆映射f-1的G-链回归点集;2)伪等价映射f的G-链回点集和G-链等价集对G强不变;3)同胚等价映射f的G-链回点集f对强不变.4)等价映射f限制在它的G-链回归点集上形成的G-链回归点集就是等价映射f在度量G-空间X上形成的G-链回归点集.这些结果丰富了拓扑群作用下度量空间中G-链回归点的理论.
According to the definition of chain recurrent point of the metric space,the concept of G-chain recurrentpoint of the metric space under the action of topological group is given and some conclusions of chain recurrent point in metric space are extended to the metric space under the action of topological group.We have the following result:1)The G-chain recurrent point set of the homeomorphic and pseudo equivalent mapping f is equal to G-chain recurrent point set of its inverse mapping f^-1;2)The G-chain recurrent point set of pseudo equivalent mapping f is strongly invariant to G and the G-chain equivalent point set of pseudo equivalent mapping f is also strongly invariant to G;3)The G-chain recurrent point set of the homeomorphic and equivalent mapping f is strongly invariant to the map f itself.4)The G-chain recurrentpoint set of the equivalent map f which is restricted in the its G-chain recurrent point set is equal to the G-chain recurrent point set of the equivalence map f in the metric G-space X.These results enrich the theory of G-chain recurrent point in the metric space under the action of topological group.
作者
冀占江
翟聪
谭伟明
JI Zhan-jiang;ZHAI Cong;TAN Wei-ming(School of Information and Electronic Engineering,Wuzhou University,Wuzhou 543002,China;Laboratory of Complex Systems Simulation and Intelligent Computing,Wuzhou University,Wuzhou 543002,China;School of Transportation and Civil Engineering and Architecture,Fo Shan University,Foshan 528000,China)
出处
《数学的实践与认识》
北大核心
2018年第23期246-250,共5页
Mathematics in Practice and Theory
基金
国家自然科学基金(41461005)
硕士学位授予单位立项建设项目(桂学位[2013]4号)
梧州学院科校级研项目(2017C001)
关键词
度量G-空间
等价映射
G-链回归点集
G-链等价集
metric G-space
equivalent mapping
G-chain recurrent point set
G-chain equivalent set
