Localization of Closedness and Continuity Properties, with Applications to Preferences and Production Sets - (Now published as 'Localisation of continuity to bounded sets for nonmetrisable vector topologies and its applications to economic equilibrium theory', in Indagationes Mathematicae (New Series), 11 (2000), pp.53-61.)

Anthony Horsley and Andrew Wrobel

STICERD - Theoretical Economics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: Localization techniques which facilitate verification of the topological properties of sets, functions and correspondences needed for equilibrium analysis in infinite-dimensional spaces are given. For example, it is shown that weak* upper semicontinuity (w*-u.s.c.) of a concave function (or a convex preorder) on the dual , L, of a separable Banach space, L, is equivalent to bounded w*-u.s.c. and therefore to sequential w*-u.s.c. For nondecreasing functions defined on bounded-from-below subsets of topological vector lattices, the property of lower semicontinuity can also be 'localized' to bounded regions, which in the case of L = L? with the Mackay topology leads to characterization in terms of sequences through the introduction of convergence measure. To illustrate the simplification this affords, Bewley's Mackey integration theory; some other uses are sketched or referred to.

Date: 1992-11
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stitep:247

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