The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets
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.
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2013-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/3648 |