Convex powerdomains II

AbstractThe study of powerdomains defined as completions via Frink ideals is continued. It is shown how to represent directed ideals ofP(D)by certain compact subsets of the original domainD, and arbitrary Frink ideals by sets of such subsets. The operations union and big union are defined and their properties studied. Finally, some results on the relationship of this powerdomain to the classical Plotkin powerdomain are presented

Convex powerdomains I

AbstractA 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