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Representation of bounded convex sets by rational convex hull of its gamma-extreme points. (English) Zbl 0817.52008

Let \(\gamma\) be a positive real number. A point \(x\) in a convex set \(C\) of a linear metric space is said to be a \(\gamma\)-extreme point of \(C\) if it does not belong to any segment whose endpoints belong to \(C\) and are at a distance greater than or equal to \(\gamma\) from \(x\). The author states some relations between extreme points and \(\gamma\)-extreme points and presents a Krein-Milman type theorem, in terms of \(\gamma\)-extreme points, for bounded (but not necessarily compact) convex sets.

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A21 Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)
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References:

[1] DOI: 10.1007/BF03014795 · JFM 42.0429.01
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