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The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets

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Author(s): I. Hetman

Journal: Carpathian Mathematical Publications
ISSN 2075-9827

Volume: 5;
Issue: 1;
Start page: 44;
Date: 2013;
Original page

Keywords: Completenes | normed spaces | topological homogeneity | closed convex sets

ABSTRACT
{We prove that an infinite-dimensional normed space $X$ is complete if and only if thespace $mathrm{BConv}_H(X)$ of all non-empty bounded closed convex subsets of $X$ istopologically homogeneous.}{completeness, normed spaces, topological homogeneity,closed convex sets
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