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L. D. Wang, “The Necessary and Sufficient Condition of a Closed Periodic Points Set of the Continuous Self-Maps of the Circle,” Journal of Shanxi Teacher’s University (Natural Science Edition), Vol. 4, No. 2, 1990 (in Chinese).

has been cited by the following article:

• 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].