Effectively giving domains

A definition of the notion of an effectively given continuous cpo is provided. The importance of the notion lies in the fact that we can readily characterize the computable (partial) functions of arbitrary finite type over an effectively given domain. We show that the definition given here is closed under several important domain constructions, namely sum, product, function space , power domain and inverse limits (the last two in a restricted form); this permits recursive domain equations to be solved effectively