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

MSC:
54E50Complete metric spaces
46E15Banach spaces of continuous, differentiable or analytic functions
54E15Uniform structures and generalizations
54C35Function spaces (general topology)