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Convex Sets, Convex Hypersurfaces, and G-Polytopes

In: On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions

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  • Paolo d’Alessandro

Abstract

In this chapter we deal with convex hypersurfaces in infinite dimension. The central result here is the well-known Convexity Theorem about convex bodies, which we will refine in various stages, culminating to its extension to convex closed sets with void interior.

Suggested Citation

  • Paolo d’Alessandro, 2025. "Convex Sets, Convex Hypersurfaces, and G-Polytopes," Springer Books, in: On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions, chapter 0, pages 427-437, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-92477-4_26
    DOI: 10.1007/978-3-031-92477-4_26
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