International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 665-668

A topological lattice on the set of multifunctions

Basil K. Papadopoulos

Democritus University of Thrace, Department of Mathematics, Xanthi 67100 , Greece

Received 1 March 1988; Revised 10 May 1988

Copyright © 1989 Basil K. Papadopoulos. 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.


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.