Piercing Hyperplane Theorem - Unveren, Burak; Barokas, Guy (PLEIADES PUBLISHING LTD, 2024)
We prove that any strictly convex and closed set in R-n is an affine subspace if it contains a hyperplane as a subset. In other words, no hyperplane fits into a strictly convex and closed set C unless C is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems.
Keywords: convex geometry; mathematical economics; Mathematics