The structure of hemispaces in \({\mathbb{R}}^ n\)

DOI10.1016/0024-3795(83)90135-0zbMath0656.52004OpenAlexW1973873191MaRDI QIDQ1110096

Ivan Singer, Juan-Enrique Martinez-Legaz

Publication date: 1988

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(83)90135-0

zbMATH Keywords

linear operatorslexicographical ordersemispaceconvex half-spacehemispace

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Axioms for convexity, The geometric structure of max-plus hemispaces, Characterization of tropical hemispaces by \((P, R)\)-decompositions, Lexicographical order, lexicographical index, and linear operators, Max-plus convex sets and max-plus semispaces. II, Step-affine functions, halfspaces, and separation of convex sets with applications to convex optimization problems, Support and separation properties of convex sets in finite dimension, Classification of semispaces according to their types in infinite-dimensional vector spaces, On \(\Phi\)-convexity of convex functions, Compatible preorders and linear operators on \({\mathbb{R}}^ n\), Contributions to max-min convex geometry. II: Semispaces and convex sets

Cites Work

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• Lexicographical order, lexicographical index, and linear operators
• The theory of convex geometries
• Lexicographical separation in \({\mathbb{R}}^ n\)
• Maximal convex sets
• The structure of semispaces
• Convex half-spaces
• Exact quasiconvex conjugation