Lenses and quasi-lenses on a space X form models of erratic non-determinism. When is equipped with quasi-metric d, there are natural quasi-metrics dP dPa the X, which resemble Pompeiu-Hausdorff metric (and contain it as subcase when d metric), tightly connected to Kantorovich-Rubinstein dKR dKRa Parts I, II III, through an isomorphism between so-called discrete normalized forks. We show that co...

1 Introduction. In 8] we showed how several issues of importance in logic programming can prootably be viewed by casting them as questions concerned with topologies on spaces of interpretations and topological continuity of operators associated with logic programs. In doing this, we were building on earlier work of Batarekh and Subrahmanian 1, 2, 3] and extending and generalising their ideas. F...

We show that a measurement μ on a continuous dcpo D extends to a measurement μ̄ on the convex powerdomain CD iff it is a Lebesgue measurement. In particular, kerμ must be metrizable in its relative Scott topology. Moreover, the space ker μ̄ in its relative Scott topology is homeomorphic to the Vietoris hyperspace of kerμ, i.e., the space of nonempty compact subsets of kerμ in its Vietoris topolog...

in this paper‎, ‎we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces‎, ‎and how the character of the remainders affects the character‎ ‎and the size of a rectifiable space‎. ‎some results in [a. v‎. ‎arhangel'skii and j‎. ‎van mill‎, ‎on topological groups with a first-countable remainder‎, ‎topology proc. 42 (2013...

We show that the space of subprobability measures, equivalently continuous valuations, on an algebraic (resp., continuous) complete quasi-metric is again and complete, when equipped with Kantorovich-Rubinstein quasi-metrics dKR (unbounded) or dKRa (bounded), themselves asymmetric forms well-known metric. also dKR-Scott dKRa-Scott topologies then coincide weak topology. obtain similar results fo...

Every Scott domain can be viewed as a generalized ultrametric space with proper ties which allow to apply a generalization of the Banach contraction mapping theorem We will give this construction in detail and apply it to a class of programs which is stricly larger than the class of all acyclic programs The paper is taken from Hit Chapter Domains as Generalized Ultrametric Spaces We rst introdu...