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The completion of the space of convex, bounded sets with respect to the Demyanov metric. (English) Zbl 1290.52004

The authors study the space of bounded convex (not necessarily closed) sets in \(\mathbb R^d\) endowed with the Demyanov (pseudo)metric and for \(d=2\) describe the completion of the induced metric space.

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
58C06 Set-valued and function-space-valued mappings on manifolds
54E50 Complete metric spaces
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