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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.

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Convex Sets, Convex Hypersurfaces, and G-Polytopes

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  • 发表日期：

    2025年

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  • Paolo d’Alessandro

摘要

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.