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- W2016376204 abstract "Let $L$ be a real (Hausdorff) topological vector space. The space $mathcal {K}[L]$ of nonempty compact subsets of $L$ forms a (Hausdorff) topological semivector space with singleton origin when $mathcal {K}[L]$ is given the uniform (equivalently, the finite) hyperspace topology determined by $L$. Then $mathcal {K}[L]$ is locally compact iff $L$ is so. Furthermore, $mathcal {K}mathcal {Q}[L]$, the set of nonempty compact convex subsets of $L$, is the largest pointwise convex subset of $mathcal {K}[L]$ and is a cancellative topological semivector space. For any nonempty compact and convex set $X subset L$, the collection $mathcal {K}mathcal {Q}[X] subset mathcal {K}mathcal {Q}[L]$ is nonempty compact and convex. $L$ is iseomorphically embeddable in $mathcal {K}mathcal {Q}[L]$ and, in turn, there is a smallest vector space $mathcal {L}$ in which $mathcal {K}mathcal {Q}[L]$ is algebraically embeddable (as a cone). Furthermore, when $L$ is locally convex, $mathcal {L}$ can be given a locally convex vector topology $mathcal {I}$ such that the algebraic embedding of $mathcal {K}mathcal {Q}[L]$ in $mathcal {L}$ is an iseomorphism, and then $mathcal {L}$ is normable iff $L$ is so; indeed, $mathcal {I}$ can be so chosen that, when $L$ is normed, the embedding of $L$ in $mathcal {K}mathcal {Q}[L]$ and that of $mathcal {K}mathcal {Q}[L]$ in $mathcal {L}$ are both iseometries." @default.
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- W2016376204 title "Hyperspaces of topological vector spaces: their embedding in topological vector spaces" @default.
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- W2016376204 doi "https://doi.org/10.1090/s0002-9939-1976-0425881-3" @default.
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