The important step to find a model for the lambda calculus is to consider only those functions (on such a partially ordered set) that are guaranteed to have least fixed points. The set of these functions, together with an appropriate ordering, is again a "domain" in the sense of the theory. But the restriction to a subset of all available functions has another great benefit: it is possible to obtain domains that contain their own function spaces, i.e. one gets functions that can be applied to themselves.