The Compactness of the Hyperspace 2X with the Locally Finite Topology

Abstract

Let X be topological space. A vietoris-type topology, called the locally finite topology, is defined on the hyperspace $2^{X}$ of all closed, nonempty subsets of X. In this paper, we discuss compactness of the locally finite topology on hyperspace. And give the important conclusion, therefore this develops E.Micheal, J.Keesling some results.