Lifting complete orders to achieve co-additivity of closure operators

We define the notion of meet-uniformity for closure operators on a complete lattice, which corresponds to co-additivity restricted to subsets mapped into the same element, and we study its properties. A class of closures given by principal filters and the downward closures are relevant examples of meet-uniform closures. Next, we introduce a lifting of a complete order by means of a meet-uniform closure. Our main results show that this lifting preserves the complete lattice structure, and allows the meet-uniform closure to become fully co-additive.