中文摘要：

证明了拓扑链遍历映射的拓扑共轭不变性;研究了f^k与f1×f2×…×fn的拓扑链遍历性,并给出了f的拓扑链遍历性与f^k的拓扑链遍历性等价的条件,以及fi,i=1,2,…,n的拓扑链遍历性与f1×f2×…×fn的拓扑链遍历性等价的条件;给出了系统（X,f）拓扑链遍历与其提升系统（X^-,f^-）的拓扑链遍历的相互蕴涵性。

英文摘要：

It is shown that maps of topological chain ergodicity is invariable under property of topological conjugate.Topological chain ergodicities of f^ k and f1×f2×…×fn are studied,and an equivalent condition of topological chain ergodicitys of f^k and f for any integer k and an equivalent condition of topological chain ergodicities of fi,i=1,2,…,and f1×f2×…×fn are given.In addition,it is shown that if（X,f） is topological chain ergodicity,then its lift map（X^～,d^～） is topological chain ergodicity.