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THE STRUCTURE OF THE NORMED LATTICE GENERATED BY THE CLOSED, BOUNDED, CONVEX SUBSETS OF A NORMED SPACE

Sims, Brailey and Bendit, Theo THE STRUCTURE OF THE NORMED LATTICE GENERATED BY THE CLOSED, BOUNDED, CONVEX SUBSETS OF A NORMED SPACE. (Submitted)

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    Abstract

    Let C(X) denote the set of all non-empty closed bounded convex subsets of a normed linear space X. In 1952 Hans R˚adstro¨m described how C(X) equipped with the Hausdorff metric could be iso-metrically embedded in a normed lattice with the order an extension of set inclusion. We call this lattice the R˚adstro¨m of X and denote it by R(X). We: (1) outline R˚adstro¨m’s construction, (2) examine the structure and properties of R(X) as a Banach space, including; completeness, density character, induced mappings, in-herited subspace structure, reflexivity, and its dual space, and (3) explore possible synergies with metric fixed point theory.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 28 Mar 2016 13:19
    Last Modified: 28 Mar 2016 13:19
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1703

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