Basil K. Papadopoulos, "A topological lattice on the set of multifunctions", International Journal of Mathematics and Mathematical Sciences, vol. 12, Article ID 236490, 4 pages, 1989. https://doi.org/10.1155/S0161171289000815
A topological lattice on the set of multifunctions
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 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 is a topological lattice.
Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.