Piercing Hyperplane Theorem

ÜNVEREN B., Barokas G.

Mathematical Notes, cilt.115, sa.3-4, ss.626-629, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 115 Sayı: 3-4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1134/s0001434624030349
  • Dergi Adı: Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.626-629
  • Anahtar Kelimeler: convex geometry, mathematical economics
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.