A "hidden" characterization of polyhedral convex sets

• Autorzy: Taras Banakh , Ivan Hetman
• Języki publikacji: EN

Abstrakty

EN

We prove that a closed convex subset C of a complete linear metric space X is polyhedral in its closed linear hull if and only if no infinite subset A ⊂ X∖ C can be hidden behind C in the sense that [x,y]∩ C ≠ ∅ for any distinct x,y ∈ A.

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 52A37: Other problems of combinatorial convexity
• 52B05: Combinatorial properties (number of faces, shortest paths, etc.)
• 52A07: Convex sets in topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 206
• Numer: 1
• Strony: 63-74

Daty

wydano

2011

Twórcy

autor

Taras Banakh

• Ivan Franko National University of Lviv, Ukraine
• Jan Kochanowski University, Kielce, Poland

autor

Ivan Hetman

• Ivan Franko National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine

Identyfikatory

DOI

10.4064/sm206-1-5