Relationships between L-ordered convergence structures and strong L-topologies

By making use of the intrinsic fuzzy inclusion orders on the fuzzy power set, the relationships between L-ordered convergence spaces and strong L-topological spaces are researched, where L is a commutative unital quantale. It is shown that the category of strong L-topological spaces can be embedded in the category of L-ordered convergence spaces as a reflective subcategory. As a result, we observe that there is a Galois correspondence between the category of L-ordered convergence spaces and the category of strong L-topological spaces. Further, it is proved that the class of all strong L-topological L-ordered convergence spaces precisely is the class of all strong L-topological spaces, and the class of spaces with non-idempotent L-ordered interior operators is characterized as a subclass of the class of L-ordered convergence spaces.