The Structure of the Normed Lattice Generated by the Closed, Bounded, Convex Subsets of a Normed Space
نویسنده
چکیده
Let C(X) denote the set of all non-empty closed bounded convex subsets of a normed linear space X. In 1952 Hans R̊adström described how C(X) equipped with the Hausdorff metric could be isometrically embedded in a normed lattice with the order an extension of set inclusion. We call this lattice the R̊adström of X and denote it by R(X). We: (1) outline R̊adström’s construction, (2) examine the structure and properties of R(X) as a Banach space, including; completeness, density character, induced mappings, inherited subspace structure, reflexivity, and its dual space, and (3) explore possible synergies with metric fixed point theory.
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