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

I. Hetman

Abstract


We prove that an infinite-dimensional normed space $X$ is complete if and only if the space $\mathrm{BConv}_H(X)$ of all non-empty bounded closed convex subsets of $X$ is topologically homogeneous.

Keywords


Completeness, normed spaces, topological homogeneity, closed convex sets

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