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The Demyanov metric in the family of convex, compact sets in finite dimensional spaces has been recently extended to the family of convex, bounded sets – not necessarily closed. In this note it is shown that these spaces are not complete and a model for the completion is proposed. A full answer is given in ℝ 2  and the situation in higher dimensions is discussed.

The completion of the space of convex, bounded sets with respect to the Demyanov metric