The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets
I. Hetman
Karpatsʹkì Matematičnì Publìkacìï · 2013
doi:10.15330/cmp.5.1.44-46 (opens in a new tab)
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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.
Abstract licence: CC BY-NC-ND
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