Boundedness and Complete Distributivity

We extend the concept of constructive complete distributivity so as to make it applicable to ordered sets admitting merely bounded suprema The KZ doctrine for bounded suprema is of some independent interest and a few results about it are given The category of ordered sets admitting bounded suprema over which inhabited classically non empty in ma distribute is shown to be bi equivalent to a category de ned in terms of idempotent relations As a corollary we obtain a simple construction of the non negative reals