关于弱混系统的注记

A note on weak mixing systems

设(X,T)是拓扑动力系统,其中X是紧致度量空间,T:X→X是连续映射.设超空间(K,d)是由X的所有非空紧子集组成的度量空间,其中d是Hausdorff度量.我们将证明对任意紧致、完全不连通集Z,都存在(K,d)中一个与Z同胚的元K,且K是传递点.

Let （X, T） be a topological dynamical system, where X is a compact metric space and T：X→X is a continuous map. We consider the hyperspace （K, d ） of all non-empty compact subsets of X endowed with the Hausdorff metric d, we will show that for any compact totally disconnected subset Z, there exists some K in K such that Z is homeomorphic to K and K is a transitive point.