Admissible domain representations of topological spaces

In this paper we consider admissible domain representations of topological spaces. A domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to D via a continuous function from E to D. We present a characterisation theorem of when a topological space has a λ-admissible and κ-based domain representation. We also prove that there is a natural cartesian closed category of countably based and countably admissible domain representations. These results are generalisations of [Sch02].