局部有限超拓扑的局部紧性

Local Compactness of Locally Finite Topology

本文讨论了赋予局部有限拓扑的非空闲子集超空间的局部紧性.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.

In this paper the local compactness of the nonempty closed subsets hyperspaces with locally finite topology is discussed. 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.