Second Descendible Self-Mapping with Closed Periodic Points Set

Abstract

Let and f : X n → X n be a continuous map. If f i s 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 y ε w ( z , f ) ∩ P ( f ) such that every point of the set orb (y,f) i s 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 condi tion of f with closed periodic set other than [ 1 ].