closure theory, powerset theory, categories of fuzzy sets

A notion of a closure theory of a powerset theory in a ground category isintroduced as a generalization of a topological theory of a powerset theory.Using examples of powerset theories in the category Set of sets and in thecategory of sets with similarity relations, it is proved that these theories canbe also used as ground theories for closure theories of powerset theories inthese two categories of fuzzy sets. Moreover, it is proved that all these closuretheories of powerset theories are topological constructs.