Towards a Convenient Category of Topological Domains

We propose acategory of topological spaces that promises to be convenient for the purposes of domain theory as amathematical the-ory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. $\mathrm{m}\mathrm{o}\mathrm{d} \dot{\mathrm{e}}\mathrm{U}\mathrm{i}\mathrm{n}\mathrm{g} $ the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide aflexible toolkit for modelling computational effects as free algebras for algebraic the-ories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is aconsequence of aconnection with realizability models