Constructing a quasi-uniform function space

Abstract

This paper attacks the problem of constructing function spaces for a convenient class of quasiuniform spaces. As, for the sake of completeness, multi-valued functions have to be considered, we define a suitable power space functor. The arising monad is a computational monad in the sense of Eugenio Moggi. The tensorial strength thus given enables us to lift the usual product to a symmetric tensor product on the Kleisli category of the monad. It is now possible to define a function space constructor yielding a symmetric monoidal closed category. As an example, we give a convenient model for the real numbers in this category.