关于赋范空间上连续自映射的回归点

在赋范空间中讨论回归点的性质，主要得到了结果：（1）如果，是序列紧赋范空间X上的连续双射，x是f的任一回归点，则对于任意整数N〉0都存在f的回归点x0∈X使得f^n（x0）=x；（2）序列紧赋范空间上连续自映射的回归点集是f的强不变子集；（3）如果f是局部连通赋范空间X上的连续自映射，则f的每一个回归点或是类周期点或是类周期点的聚点．作为推论，在实直线段上得到了类似的结论．

The reurrent points of continuous self-maps on a normed space

This paper mainly discusses some properties of the recurrent points of a continuous mapping from a normed space X to oneself . The following results are showed:(1) Let f be a surjective and injective continuous self-mapping from a sequentially compact normed space X to oneself, if x is a recurrent point of f,then there is some recurrent points x0 of such that fn(x0) = x for every positive integer n;(2) If f is a continuous mapping from sequentially compact normed space to oneself, then the set of all recurr...