Geometric Form of the Hahn–Banach Theorem for Generalized Convexity
Copyright policy )Geometric Form of the Hahn–Banach Theorem for Generalized Convexity
The article deals with a class of compact sets \(K\subset {\mathbb R}^n\) that are convex with respect to some family \(A\) of \(m\)-planes. For compact sets satisfying conditions of acyclicity of intersections with a certain set of two-dimensional planes their generalized \((n,n-2;A)\)-convexity is proved.
- National Academy of Sciences of Ukraine Ukraine
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
Axiomatic and generalized convexity, generalized convexity, Euclidean \(n\)-space, compact set, Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.), Theorems of Hahn-Banach type; extension and lifting of functionals and operators, family of planes, Convex sets in \(n\) dimensions (including convex hypersurfaces)
Axiomatic and generalized convexity, generalized convexity, Euclidean \(n\)-space, compact set, Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.), Theorems of Hahn-Banach type; extension and lifting of functionals and operators, family of planes, Convex sets in \(n\) dimensions (including convex hypersurfaces)
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