Piercing Hyperplane Theorem
Mathematical Notes, cilt.115, sa.3-4, ss.626-629, 2024 (SCI-Expanded, Scopus)
- 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.