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. doi: 10.6054/j.jscnun.2022034
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. doi: 10.6054/j.jscnun.2022034
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. doi: 10.6054/j.jscnun.2022034
Citation: 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. doi: 10.6054/j.jscnun.2022034

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

  • 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: XX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: XX同胚伪等价,则f(SCRG(f))=SCRG(f); (3)设(X, d)是紧致度量G-空间,f: XX同胚伪等价且度量d对群G不变,则SCRG(f)=SCRG(f-1)。

     

    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: XX 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: XX be an homeomorphic pseudoequivalent map; then f(SCRG(f))=SCRG(f); (3) Let(X, d)be a compact metric G-space, f: XX be an homeomorphic pseudoequivalent map and the metric d be invariant to group G; then SCRG(f)=SCRG(f-1).

     

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