and pointed whenever Q is pointed.Thus the complete partial orders with Scott-continuous maps form a cartesian closed category.

Every order-preserving self-map f of a pointed dcpo (P, ?) has a least fixed-point. If f is continuous then this fixed-point is equal to the supremum of the iterates (?, f(?), f(f(?)), ... fⁿ(?), ...) of ? (see also the Kleene fixed-point theorem).