No abstract

No abstract

No abstract

No abstract

No abstract

Abstract. The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0, +∞) ω . Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of a quasi-normed semilinear space provides a suitable setting to carry out an analysis of the dual complexity space. We show that if (E, . ) is a biBanach space (i.e., a quasi-normed space whose induced quasi-metric is bicomplete), then the function space (B * E , . B * ) is biBanach, where B *< +∞}, and f B * = ∞ n=0 2 −n f (n) . We deduce that the dual complexity space admits a structure of quasinormed semlinear space such that the induced quasi-metric space is order-convex, upper weightable and Smyth complete, not only in the case that this dual is a subspace of [0,+∞) ω but also in the general case that it is a subspace of F ω where F is any biBanach normweightable space. We also prove that for a large class of dual complexity (sub)spaces, lower boundedness implies total boundedness. Finally, we investigate completeness of the quasi-metric of uniform convergence and of the Hausdorff quasi-pseudo-metric for the dual complexity space, in the context of function spaces and hyperspaces, respectively.2000 AMS Classification: 54E50, 54E15, 54C35, 46E15.

Stable partial metric spaces form a fundamental concept in Quantitative Domain Theory. Indeed, all domains have been shown to be quantifiable via a stable partial metric.Monoid operations arise naturally in a quantitative context and hence play a crucial role in several applications. Here, we show that the structure of a stable partial metric monoid provides a suitable framework for a unified approach to some interesting examples of monoids that appear in Theoretical Computer Science. We also introduce the notion of a semivaluation monoid and show that there is a bijection between stable partial metric monoids and semivaluation monoids.

No abstract