The Cartesian Closed Topological Hull of the Category of Approach Uniform Spaces

Abstract

The category AUnif of approach uniform spaces and uniform contractions properly combines uniform spaces and extended pseudo-metric spaces but (like Unif) lacks convenience, such as cartesian closedness. This paper therefore considers its cartesian closed topological hull, which is first described as a subcategory of SAULim, the category of semi-approach uniform limit spaces and uniform contractions. This hull is then also given a description inside the topological universe hull of AUnif and is shown to be a reasonable generalization of the corresponding hull of Unif. Furthermore, some referencing notes are provided with respect to similar results that can be obtained when starting from qAUnif (where symmetry assumptions are omitted).