Let (L , * , 1) be a residuated complete lattice with the underlying lattice L a meet continuous lattice. This paper presents a systematic investigation of the interrelationship between the categories of limit spaces, L-topological spaces, and L-preorders. The results exhibit a close connection between these different mathematical structures.
Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the… (More)