[17T] Topics:separation,support. Prerequisites: [170]↺↻,[17J]↺↻, [17B]↺↻.
Given \(A⊂ ℝ^ n\) convex non-empty and \(z∈ ∂ A\), prove that there exist \(v∈ℝ^ n,a∈ℝ\) such that \(⟨ z,v⟩= a\) and \(∀ x∈ A,⟨ x,v⟩≤ a\). The hyperplane thus defined is called support hyperplane of \(z\) for \(A\).
[17V]↺↻
