Cartesian closed hull of the category of uniform spaces (Q1071342)

The author studies the category of bornological uniform spaces. The objects are uniform spaces endowed with a bornology (and collection of so called bounded subsets of the underlying set which contains all finite sets and is closed under subsets and finite unions), and the morphisms are uniformly continuous mappings preserving bounded sets. The authors show that the category of bornological uniform spaces is the smallest cartesian closed category with initial structures containing the category of uniform spaces Unif as a full finitely productive subcategory such that its forgetful functor extends that of Unif, i.e. that the category of bornological uniform spaces is a cartesian closed topological hull of Unif.