The Cartesian Closed Topological Hull of the Category of (Quasi-)Uniform Spaces (Revisited)

Abstract

This paper provides a concrete description of the cartesian closed topological hull of qUnif, the category of quasi-uniform spaces and uniformly continuous maps, inside q(S)ULim, the category of quasi-(semi-)uniform limit spaces and uniformly continuous maps, which also allows to derive a similar and new description of the CCT hull of Unif inside (S)ULim. In both cases, the objects of the CCT hull are (quasi-)(semi-)uniform limit spaces whose collection of filters satisfies some natural closure condition, related to the (q)Unif-bireflection of the space in question.