中文摘要：

首先讨论了在强一致收敛下极限系统的轨道闭包、回归点集以及极小点集与序列系统中的相应集合之间的关系，并通过举例说明在一致收敛条件下没有上述相应结果．然后，我们利用这些结果给出了拓扑传递性、极小性及区间上周期点稠密性关于强一致收敛遗传性的不同于文献中曾几平等人的另一种证明．

英文摘要：

In this paper, we first study the relationships of the orbit closure, the recurrence set and minimal points set between the dynamical systems sequence and the limit system under strongly uniform convergence, and give some counterexamples to show they are wrong under uniform convergence. Then, we use another method that different from Zeng Fan-ping, et al＇s to prove the topological transitivity, the minimality and the denseness of the oeriodic in interval can be inherted bv strongly uniform convergence.