赋予hit—or-miss拓扑超空间动力系统的拓扑熵

设（X，d，f）为拓扑动力系统，其中X为局部紧第二可数Hausdorff空间，d为紧型度量，f为完备映射，用2^x和f分别表示由X的所有非空闭子集和所有闭子集构成的集族，（2^x，ρ，2^f）和（f，ρ，2^f）为由（X，d，f）诱导的赋予hit—or—miss拓扑的超空间动力系统．本文研究了h（X，d，f）和h（2^...

Topological entropy of induced hyperspace dynamical systems equipped with the hit-or-miss topology

Let （X, d, f） be a topological dynamical system, where X is a Hausdorff locally compact second countable space, d is a compact-type metric and f is a perfect mapping. Let F （resp., 2x） be the space of all closed subsets （resp., all non-empty closed subsets） of X equipped with the hit-or-miss topology. Let （F, ρ, 2f） and （2x, ρ, 2f） denote the hyperspace dynamical systems induced by （X, d, f）. In this papper, the authors studied the relationship between h（X, d, f） and h（2X, p, 2f） （resp., h（F, ρ, 2f）, whenever （F, ρ, 2f） exists）. In addition, a sufficient condition was provided to demonstrate that h（2x, ρ, 2f） （resp., h（F, p, 2f）, whenever （F, ρ, 2f） exists） is infinity. These conclusions enriched the contents of induced hyperspace dyrnamical systems equipped with the hit-or-miss topology.