Ideal-valued topological structures

With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M-valued L-topological spaces (i.e. (L,M)-topological spaces) and Idl(M)-valued L-topological spaces where Idl(M) is the complete lattice of all ideals of M. It is shown that the right adjoint functor provides a procedure of generating (L,M)-topologies from antitone families of (L,M)-topologies. This procedure is then applied to give an internal characterization of joins in the complete lattice of all (L,M)-topologies on a given set. © 2010 Elsevier B.V. All rights reserved.