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

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, and f: X→X be an homeomorphic pseudoequivalent map; then f(SCR_G(f))=SCR_G(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 SCR_G(f)=SCR_G(f^-1).