Set-Valued Analysis

, Volume 12, Issue 1–2, pp 61–77 | Cite as

Constructible Convex Sets

  • Jonathan M. Borwein
  • Jon D. Vanderwerff


We investigate when closed convex sets can be written as countable intersections of closed half-spaces in Banach spaces. It is reasonable to consider this class to comprise the constructible convex sets since such sets are precisely those that can be defined by a countable number of linear inequalities, hence are accessible to techniques of semi-infinite convex programming. We also explore some model theoretic implications. Applications to set convergence are given as limiting examples.

convex sets countable intersections biorthogonal systems Mosco convergence slice convergence Martin's axiom Kunen's space 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Jonathan M. Borwein
    • 1
  • Jon D. Vanderwerff
    • 2
  1. 1.Centre for Experimental and Constructive MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of MathematicsLa Sierra UniversityRiversideUSA

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