Convex powerdomains I

A completion via Frink ideals is used to define a convex powerdomain of an arbitrary continuous lattice as a continuous lattice. The powerdomain operator is a functor in the category of continuous lattices and continuous inf-preserving maps and preserves projective limits and surjectivity of morphisms; hence one can solve domain equations in which it occurs. Analogous results hold for algebraic lattices and bounded complete algebraic cpo's.