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 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).