Normability via the Convergence of Closed and Convex Sets

S. Dancs (), P. Medvegyev () and Gyula Magyarkuti ()
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S. Dancs: Corvinus University of Budapest
P. Medvegyev: Corvinus University of Budapest

Journal of Optimization Theory and Applications, 2011, vol. 150, issue 3, No 13, 675-682

Abstract: Abstract The purpose of this short technical note is to show that a locally convex topological vector space is normable, if and only if an important convergence theorem about closed and convex sets holds. This new assumption of normability is related to the problem of preservation of Hausdorff lower continuity of the intersection of Hausdorff lower continuous, closed and convex valued correspondences.

Keywords: Normability; Hypertopologies; Continuity of intersection of correspondences; Lower Hausdorff topology; Lower Vietoris topology; Kuratowski limit (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-011-9835-1

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