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

Katsuro Sakai¹ ; Zhongqiang Yang²

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.

Résumé

Let ${\mathrm{Conv}}_F({\mathbb{R}}^n)$ be the space of all non-empty closed convex sets in Euclidean space ${\mathbb{R}}^n$ endowed with the Fell topology. We prove that ${\mathrm{Conv}}_F({\mathbb{R}}^n)\approx {\mathbb{R}}^n\times Q$ for every $n>1$ whereas ${\mathrm{Conv}}_F(\mathbb{R})\approx \mathbb{R}\times \mathbb{I}$.

Détail

DOI : 10.4064/ba55-2-4

Mots-clés : 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