Cartesian-closedness and Subcategories of (L,M)-fuzzy Q-convergence Spaces

In this paper, we first construct the function space of ( L,M )-fuzzy Q-convergence spaces to show the Cartesian-closedness of the category ( L,M )- QC of ( L,M )-fuzzy Q-convergence spaces. Secondly, we introduce several subcategories of ( L,M )- QC , including the category ( L,M )- KQC of ( L,M )-fuzzy Kent Q-convergence spaces, the category ( L,M )- LQC of ( L,M )-fuzzy Q-limit spaces and the category ( L,M )- PQC of ( L,M )-fuzzy pretopological Q-convergence spaces, and investigate their relationships.

Some New Intrinsic Topologies on Complete Lattices and the Cartesian Closedness of the Category of Strongly Continuous Lattices

We prove some new characterizations of strongly continuous lattices using two new intrinsic topologies and a class of convergences. Lastly we show that the category of strongly continuous lattices and Scott continuous mappings is cartesian closed.

WHEN IS A CATEGORY OF MANY-SORTED PARTIAL ALGEBRAS CARTESIAN-CLOSED?

In this paper we study the cartesian closedness of the five most natural categories with objects all partial many-sorted algebras of a given signature. In particular, we prove that, from these categories, only the usual one and the one having as morphisms the closed homomorphisms can be cartesian closed. In the first case, it is cartesian closed exactly when the signature contains no operation symbol, in which case such a category is a slice category of sets. In the second case, it is cartesian closed if and only if all operations are unary. In this case, we identify it as a functor category and we show some relevant constructions in it, such as its subobjects classifier or the exponentials.