Metrization of Multifunction Spaces

In this paper, the relations among the point-compact continuous multifunction spaces under compact-open topology, uniform convergence topology, uniform convergence topology on compacta and metric topology, from a topology space to a metric space, are investigated. Some equivalent results about the point-compact continuous multifunction spaces, which are metrizable from a topological space to the real line with compact-open topology, are obtained by using induced mappings and embedding mappings. These results generalize corresponding results concerning continuous single-valued function spaces to the point-compact continuous multifunction spaces.