The Hyperplane Separation Theorem is a fundamental result in convex geometry and functional analysis that deals with the separation of convex sets in a Euclidean space.
Articles by others on the same topic
Two nonempty disjoint convex sets in a finite-dimensional real vector space admit a separating nonzero linear functional: for an appropriate and , on the respective sets. Strict separation requires additional assumptions, such as one set being compact and the other closed. For an open convex cone excluding zero, separation from gives for all ; scaling cone elements forces the separating level to be zero. This finite-dimensional result is related to the supporting hyperplane theorem.