Ideal-valued topological structures (Q622027)

With \(L\) a complete lattice and \(M\) a continuous lattice, this paper demonstrates an adjunction between \((L, M)\)- and \((L,\text{Idl}(M))\)-topological spaces; it is shown that the right adjoint functor provides a procedure of generating \((L, M)\)-topologies from antitone families of \((L, M)\)-topologies and how \((L,\text{Idl}(M))\)-topologies can be used to give an internal characterization of joins of \((L, M)\)-topologies. This paper is a sequel to the paper [\textit{T. Kubiak} and \textit{A. P. Šostak}, Quaest. Math. 20, No. 3, 423--429 (1997; Zbl 0890.54005)], where \(\text{Low}(M)\) with a completely distributive lattice \(M\) is used instead of \(\text{Idl}(M)\) (from the authors's abstract).