A topological lattice on the set of multifunctions

Abstract

Let X be a Wilker space and M(X,Y) the set of continuous multifunctions from X to a topological space Y equipped with the compact-open topology. Assuming that M(X,Y) is equipped with the partial order ⊂ we prove that (M(X,Y),⊂) is a topological V-semilattice. We also prove that if X is a Wilker normal space and U(X,Y) is the set of point-closed upper semi-continuous multifunctlons equipped with the compact-open topology, then (U(X,Y),⊂) is a topological lattice.