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Minimal pairs of bounded closed convex sets. (English) Zbl 0896.52002

The authors consider minimal presentations for members of the space of bounded closed convex sets. They prove existence of a minimal pair in the case when the underlying space is reflexive and give an example of nonreflexive Banach space in which this property fails.

MSC:

52A07 Convex sets in topological vector spaces (aspects of convex geometry)
26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
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