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