Piercing Hyperplane Theorem

ÜNVEREN B., Barokas G.

Mathematical Notes, vol.115, no.3-4, pp.626-629, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 115 Issue: 3-4
  • Publication Date: 2024
  • Doi Number: 10.1134/s0001434624030349
  • Journal Name: Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.626-629
  • Keywords: convex geometry, mathematical economics
  • Yıldız Technical University Affiliated: Yes

Abstract

Abstract: We prove that any strictly convex and closed set in 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 unless is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems.