Geodesic
The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology
Katsuro Sakai 1   ; Zhongqiang Yang 2
1 Institute of Mathematics University of Tsukuba Tsukuba, 305-8571, Japan
2 Department of Mathematics Shantou University Shantou, Guangdong 515063, P.R. China
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 2, pp. 139-143 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\mathop{\rm Conv}_F(\mathbb R) \approx \mathbb R\times \mathbb I$.
DOI : 10.4064/ba55-2-4
Keywords: mathop conv mathbb space non empty closed convex sets euclidean space mathbb endowed fell topology prove mathop conv mathbb approx mathbb times every whereas mathop conv mathbb approx mathbb times mathbb

Katsuro Sakai  1   ; Zhongqiang Yang  2

1 Institute of Mathematics University of Tsukuba Tsukuba, 305-8571, Japan
2 Department of Mathematics Shantou University Shantou, Guangdong 515063, P.R. China 
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     title = {The {Spaces} of {Closed} {Convex} {Sets} in {Euclidean} {Spaces
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     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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Katsuro Sakai; Zhongqiang Yang. The Spaces of Closed Convex Sets in Euclidean Spaces
 with the Fell Topology. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 2, pp. 139-143. doi: 10.4064/ba55-2-4

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