Duality and quasi-normability for complexity spaces. (English) Zbl 1022.54018

Romaguera, Salvadore; Schellekens, Michel

Appl. Gen. Topol. 3, No. 1, 91-112 (2002).

The authors continue their study of dual complexity spaces, see [Topology Appl. 98, 311-322 (1999; Zbl 0941.54028)]. In particular, they show that the dual complexity space (in the general case where it is considered a subspace of \(F^\omega\), where \(F\) is any bi-Banach norm-weightable space) admits the structure of a quasi-normed semilinear space such that the induced quasi-metric space is order-convex, upper weightable and Smyth complete. They also investigate completeness of the quasi-metric of uniform convergence and of the Hausdorff quasi-pseudometric for the dual complexity space, in the context of function spaces and hyperspaces, respectively.

Reviewer: Hans Peter Künzi (Rondebosch)

MSC:

54E50	Complete metric spaces
46E15	Banach spaces of continuous, differentiable or analytic functions
54E15	Uniform structures and generalizations
54C35	Function spaces in general topology

Keywords:

complexity space; quasi-norm; quasi-metric; bi-Banach space; Smyth complete

Citations:

Zbl 0941.54028