Displaying similar documents to “On Convex Sets with Convex-Hereditary CEP”

A "hidden" characterization of polyhedral convex sets

Taras Banakh, Ivan Hetman (2011)

Studia Mathematica

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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.

Paraconvex functions and paraconvex sets

Huynh Van Ngai, Jean-Paul Penot (2008)

Studia Mathematica

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We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded....