| 在度量空间中几个点集的一点注记 |
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| 引用本文： | 李春霞,金渝光.在度量空间中几个点集的一点注记[J].周口师范学院学报,2012,29(5):5-6. |
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| 作者姓名： | 李春霞 金渝光 |
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| 作者单位： | 重庆师范大学数学学院,重庆,400047 |
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| 基金项目： | 国家自然科学基金资助项目(No.10971240) |
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| 摘 要： | 将实线段上连续自映射的w-极限点集和几个周期点集推广到度量空间中,得出两个结果：（1）设X是序列紧度量空间,f：X→X是连续的一一映射,如果y∈X是f的w-极限点,则n∈N＋,都存在f的w-极限点x0∈X,使得fn（x0）=y;（2）在度量空间中,周期点集与终于周期点集的并集等于准周期点集.即P（f）∪E′P（f）=EP（f）.
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| 关 键 词： | 度量空间 w-极限点 周期点 终于周期点集 准周期点集 |
A little note about several point sets in the metric space |
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| LI Chunxia,JIN Yuguang.A little note about several point sets in the metric space[J].Journal of Zhoukou Normal University,2012,29(5):5-6. |
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| Authors: | LI Chunxia JIN Yuguang |
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| Institution: | (College of Mathematics,Chongqing Normal University,Chongqing 400047,China) |
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| Abstract: | The real segment on a continuous self-maps of the w-limit point set and several periodic point sets is extended to the metric space,two results are obtained:(1)Let X be a coutably compact metric space,f:X→X is one one coutinous mapping.If y∈X is w-limit point of f,then x∈N+,there are w-limit point x0∈X of f,fn(x0)=y is maked.(2)In a metric space,the set of periodic points and eventually periodic point set and equal to the quasi periodic point set,It is:P(f)∪E′P(f)=EP(f). |
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| Keywords: | coutably compact space w-limit point periodic point set eventually periodic point set quasi periodic point set |
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