| 度量G-空间中G-强链回归点集的动力学性质 |
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| 引用本文： | 冀占江.度量G-空间中G-强链回归点集的动力学性质[J].华南师范大学学报(自然科学版),2022,54(2):115-119. |
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| 作者姓名： | 冀占江 |
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| 作者单位： | 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 |
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| 基金项目： | 广西自然科学基金项目(2020JJA110021)； |
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| 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SCRG(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(SCRG(f))=SCRG(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SCRG(f)=SCRG(f-1)。
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| 关 键 词： | 度量G-空间 伪等价映射 G-强链回归点 |
| 收稿时间： | 2021-04-24 |
The Dynamical Property of G-Strong Chain Recurrent Point Set in Metric G-space |
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| JI Zhanjiang.The Dynamical Property of G-Strong Chain Recurrent Point Set in Metric G-space[J].Journal of South China Normal University(Natural Science Edition),2022,54(2):115-119. |
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| Authors: | JI Zhanjiang |
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| Institution: | 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 |
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| Abstract: | 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 SCRG(f) is a closed set; (2) Let (X, d) be a compact metric G-space, G be a compact topological group, and f: X→X be an homeomorphic pseudoequivalent map; then f(SCRG(f))=SCRG(f); (3) Let(X, d)be a compact metric G-space, f: X→X be an homeomorphic pseudoequivalent map and the metric d be invariant to group G; then SCRG(f)=SCRG(f-1). |
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