TITLE:
Second Descendible Self-Mapping with Closed Periodic Points Set
AUTHORS:
Gengrong Zhang, Zhanjiang Ji, Fanping Zeng
KEYWORDS:
Periodic Point; Recurrent Point; w-Limit Point; Second Descendible Map
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.7,
June
28,
2013
ABSTRACT:
Let and f:Xn→Xn be a continuous map. If f is a second descendible map,
then P(f) is closed if and only if
one of the following hold: 1) ; 2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point of
the set orb (y,f) is a isolated point of the
set w (z,f); 3) For any z ε R(f), the set w (z,f) is finite; 4) For any z ε R(f), the set w' (z,f) is finite. The consult give
another condition of f with closed periodic set
other than [1].