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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 of the space $C o n v_{} (X)$ of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex...

A "hidden" characterization of polyhedral convex sets

Taras Banakh, Ivan Hetman (2011)

Studia Mathematica

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.

We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.

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A bipolar theorem for L $_{+}^{0} (Ω, ℱ, 𝐏)$

A Choquet Ordering and Unique Decompositions in Convex sets of Tight Measures

A compact convex set with no extreme points

A Dini principle for convex functions and the theorem of James

A General Approach to the Notion of Silov Boundary.

A general continuity principle

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

A "hidden" characterization of polyhedral convex sets

A new concept of separation

A new tool in the theory of integral representation.

A new type of affine Borel function.

A noncompact Choquet theorem

A Note on Extreme Positive Definite Matrices.

A note on intersections of simplices

A Potential-Theoretic Approach to Parallel Addition.

A Re-Examination of the Roberts Example of a Compact Convex Set Without Extreme Points.

A refinement of the Helson-Szegö theorem and the determination of the extremal measures

A remark on Edgar's extremal integral representation theorem

A stability theorem for the choquet-ordering in C...(X).

A study on some new types of Hardy-Hilbert's integral inequality.

Currently displaying 1 – 20 of 244