证明了拓扑链遍历映射的拓扑共轭不变性；研究了fk与f1×f2×…×fn的拓扑链遍历性,并给出了f的拓扑链遍历性与fk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.%It is shown that maps of topological chain ergodicity is invariable under property of topological conjugate. Topological chain ergodicities of fk and f1×f2 × … ×fn are studied, and an equivalent condition of topological chain ergodicitys of fk 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.
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