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Grzybowski, Jerzy; Leśniewski, Andrzej; Rzeżuchowski, Tadeusz

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

Demonstr. Math. 46, No. 1, 191-196 (2013).
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.
Reviewer: Taras Banakh (Lviv)

Cited in 1 Document

MSC:

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

Keywords:

convex and bounded sets; Demyanov metric; Hausdorff metric; completion of metric spaces
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\textit{J. Grzybowski} et al., Demonstr. Math. 46, No. 1, 191--196 (2013; Zbl 1290.52004)
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