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Normability via the Convergence of Closed and Convex Sets

Author

Listed:
  • S. Dancs

    (Corvinus University of Budapest)

  • P. Medvegyev

    (Corvinus University of Budapest)

  • Gy. Magyarkuti

    (Corvinus University of Budapest)

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.

Suggested Citation

  • S. Dancs & P. Medvegyev & Gy. Magyarkuti, 2011. "Normability via the Convergence of Closed and Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 675-682, September.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:3:d:10.1007_s10957-011-9835-1
    DOI: 10.1007/s10957-011-9835-1
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