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The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets ([27]). In the present paper we summarize the known results, generalize some of them and add new ones.

Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski–Rådström–Hörmander spaces