The main result is as follows: Let X be a regular space, then the nonempty closed subsets hyperspace is locally compact iff X can be represented as the sum of a compact space and a discrete space.

• 主要结果是：X正则，则其闭子集超空间局部紧当且仅当X可表示成一个紧空间与一个离散空间的拓扑和。