On generalized topological molecular lattices

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and define a closed element by the pseudocomplement of an open element.  We have two structures on a completely distributive complete lattice, topology and generalized co-topology which are not dual to each other. We study the basic concepts, in particular separation axioms and some relations among them.