The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology

Volume 55 / 2007

Katsuro Sakai, Zhongqiang Yang Bulletin Polish Acad. Sci. Math. 55 (2007), 139-143 MSC: 54B20, 54D05, 54E45, 57N20. DOI: 10.4064/ba55-2-4


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 $\mathop{\rm Conv}_F(\mathbb R) \approx \mathbb R\times \mathbb I$.


  • Katsuro SakaiInstitute of Mathematics
    University of Tsukuba
    Tsukuba, 305-8571, Japan
  • Zhongqiang YangDepartment of Mathematics
    Shantou University
    Shantou, Guangdong
    515063, P.R. China

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