Kantorovich-Rubinstein quasi-metrics II: Hyperspaces and powerdomains

We show that the Kantorovich-Rubinstein quasi-metrics dKR and dKRa of Part I extend naturally to various spaces previsions, in particular not just linear previsions (roughly, measures) I. There are natural isomorphisms between Hoare Smyth powerdomains, as used denotational semantics, discrete sublinear normalized superlinear respectively. Turning corresponding hyperspaces, namely same but equipped with lower Vietoris upper topologies instead, this turns into homeomorphisms space so-called weak topology. Through these again, two powerdomains inherit dH dQ, respectively, reminiscent well-known Hausdorff metric. Then we an algebraic complete quasi-metric again complete, those quasi-metrics, similarly continuous complete. Furthermore, case, dH-Scott topology coincides topology, dQ-Scott