The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 139-143
MSC: 54B20, 54D05, 54E45, 57N20.
DOI: 10.4064/ba55-2-4
Abstract
Let $\mathop{\rm Conv}_F(\mathbb R^n)$ be the space of all non-empty closed convex sets in Euclidean space $\mathbb R^n$ endowed with the Fell topology. We prove that $\mathop{\rm Conv}_F(\mathbb R^n) \approx \mathbb R^n \times Q$ for every $n > 1$ whereas $\mathop{\rm Conv}_F(\mathbb R) \approx \mathbb R\times \mathbb I$.
