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Zbl 1022.54018
Romaguera, Salvadore; Schellekens, Michel
Duality and quasi-normability for complexity spaces. (English)
[J] Appl. Gen. Topol. 3, No.1, 91-112 (2002). ISSN 1576-9402

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.
[Hans Peter Künzi (Rondebosch)]

MSC 2000:: *54E50 Complete metric spaces
46E15 Banach spaces of functions defined by smoothness properties
54E15 Uniform structures and generalizations
54C35 Function spaces (general topology)

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

Citations: Zbl 0941.54028

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