Topological classification of the hyperspaces of polyhedral convex sets in normed spaces

Author I. V. Hetman
ihromant@gmail.com
Ivan Franko National University of Lviv

Abstract We prove that, for a normed space $X$ of dimension $\dim(X)\ge 2$ the space $\mathrm{PConv}_H(X)$ of non-empty polyhedral convex subsets of $X$ endowed with the Hausdorff metric is homeomorphic to the topological sum $\{0\}\oplus |X^*|\times (\mathbb R\oplus (\mathbb R\times\bar{\mathbb{R}}_+)\oplus l_2^f)$, where the cardinal $|X^*|$ is endowed with the discrete topology.
Keywords hyperspace; polyhedral convex set
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Pages 203-211
Volume 39
Issue 2
Year 2013
Journal Matematychni Studii
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