The Cartesian closedness of the category Fuzz and function spaces on topological fuzzes
In some works the category Fuzz consisting of all fuzzes, i.e., all completely distributive lattices with an order reversing involution and all order homomorphisms has been studied and fuzzes topologized. In this paper function spaces are defined on topological fuzzes and the category Fuzz is proved to be Cartesian closed. To study the Cartesian closedness of Fuzz, it is necessary to prove that this category has exponents. To do so, the set of all mappings preserving arbitrary joins is considered and the concept of parallelism of two mappings is introduced. To study function spaces on topological fuzz, the concept of subspaces of a topological fuzz is introduced. Topologies of pointwise convergence and uniform convergence are defined and discussed.
scientific article; zbMATH DE number 788354