Second Descendible Self-Mapping with Closed Periodic Points Set

Gengrong Zhang, Zhanjiang Ji, Fanping Zeng

College of Mathematics and Information Science, Guangxi University, Nanning, China.

DOI: 10.4236/am.2013.47133                

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].

Keywords

Periodic Point; Recurrent Point; w-Limit Point; Second Descendible Map

Conflicts of Interest

The authors declare no conflicts of interest.

References

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