Let （X, d） be a metric space and f be a continuous map from X to X. Denote by EP（f） and Ω（f） the sets of eventually periodic points and non-wandering points of f, respectively. It is well known that for a tree ...Let （X, d） be a metric space and f be a continuous map from X to X. Denote by EP（f） and Ω（f） the sets of eventually periodic points and non-wandering points of f, respectively. It is well known that for a tree map f, the following statements hold： （1） If x ∈ Ω（f） - Ω（f^n） for some n ≥ 2, then x ∈ EP（f）. （2） Ω（f） is contained in the closure of EP（f）. The aim of this note is to show that the above results do not hold for maps of dendrites D with Card（End（D）） = No （the cardinal number of the set of positive integers）.展开更多
基金Supported by NSFC(Grant Nos.11461003,11261005)NSF of Guangxi(Grant No.2014GXNSFBA118003)
文摘Let （X, d） be a metric space and f be a continuous map from X to X. Denote by EP（f） and Ω（f） the sets of eventually periodic points and non-wandering points of f, respectively. It is well known that for a tree map f, the following statements hold： （1） If x ∈ Ω（f） - Ω（f^n） for some n ≥ 2, then x ∈ EP（f）. （2） Ω（f） is contained in the closure of EP（f）. The aim of this note is to show that the above results do not hold for maps of dendrites D with Card（End（D）） = No （the cardinal number of the set of positive integers）.
