Displaying similar documents to “An example of J. W. Roberts of a convex compact subset in a linear metric space with no extreme points”

The Demyanov metric and some other metrics in the family of convex sets

Tadeusz Rzeżuchowski (2012)

Open Mathematics

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We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.

Strictly convex metric spaces with round balls and fixed points

Inese Bula (2005)

Banach Center Publications

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The paper introduces a notion of strictly convex metric space and strictly convex metric space with round balls. These objects generalize the well known concept of strictly convex Banach space. We prove some fixed point theorems in strictly convex metric spaces with round balls.

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.