The compact~*-topology of multifunction spaces

A kind of topology,e.g.,compact *-topology,was introduced.When range space is uniform space,a sufficient condition about upper semi-*-continuous and lower semi-*-continuous multifunction was given.When range space is strong uniform space,a sufficient and necessary condition about upper semi-*-continuous and lower semi-*-continuous multifunction was given.It was proved that compact *-topology is finer than the compact-open topology of multifunction spaces when every multifunction was point compact,and that uniform convergence topology on a family of compact sets is finer than the compact *-topology of multifunction spaces.