Topological Representation of the -calculus

The-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from category theory, the usual calculus of-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a \minimal" topological model, in which every continuous function is-deenable. These results subsume earlier ones using cartesian closed categories, as well as those employing so-called Henkin and Kripke-models.