Support, Convexity Conditions and Convex Hypersurfaces in Infinite\n Dimension

2019/09/15 by Paolo D’Alessandro, d'Alessandro, Paolo
Computer Science · Mathematics · #52A07 #53B10 #53D99 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1909.06768

openalex publication_date 2019/09/15 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Working in infinite dimensional linear spaces, we deal with support for\nclosed sets without interior. We generalize the Convexity Theorem for closed\nsets without interior. Finally we study the infinite dimensional version of\nJordan hypersurfaces. Our whole work never assumes smoothness and is based\nexclusively on non-differential Convex Analysis tools and, in particular, on\ntheory of convex cones. A crucial mathematical tool for our results is obtained\nsolving the decomposition problem for non-closed non pointed cones.\n

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