A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces

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

Abstrakty

EN

A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component 𝓗 of the space $Conv_{𝖧}(X)$ of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if 𝓗 contains a polyhedral convex set.

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 52A27: Approximation by convex sets
• 52A37: Other problems of combinatorial convexity
• 46N10: Applications in optimization, convex analysis, mathematical programming, economics
• 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: 2012
• Tom: 210
• Numer: 2
• Strony: 137-157

Daty

wydano

2012

Twórcy

autor

Taras Banakh

• Ivan Franko National University of Lviv, Lviv, Ukraine
• Uniwersytet Jana Kochanowskiego, Kielce, Poland

autor

Ivan Hetman

• Ivan Franko National University of Lviv, Lviv, Ukraine

Identyfikatory

DOI

10.4064/sm210-2-3