Hyperspaces with the Hausdorff Metric and Uniform ANR's

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概要

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• For a metric space X =(X, d), let \Cld_H(X) be the space of all nonempty closed sets in X with the topology induced by the Hausdorff extended metric: d_H(A, B) =max\bigg{\sup<SUB>x∈ B</SUB>d(x, A), \ \sup<SUB>x∈ A</SUB>d(x, B)\bigg} ∈ [0, ∞]. On each component of \Cld_H(X), d_H is a metric (i.e., d_H(A, B) < ∞). In this paper, we give a condition on X such that each component of \Cld_H(X) is a uniform AR (in the sense of E.Michael). For a totally bounded metric space X, in order that \Cld_H(X) is a uniform ANR, a necessary and sufficient condition is also given. Moreover, we discuss the subspace \Dis_H(X) of \Cld_H(X) consisting of all discrete sets in X and give a condition on X such that each component of \Dis_H(X) is a uniform AR and \Dis_H(X) is homotopy dense in \Cld_H(X).

• 社団法人 日本数学会の論文
• 2005-04-01

著者

• Sakai Katsuro

  Institute Of Mathematics University Of Tsukuba

• Yaguchi Masato

  Institute Of Mathematics University Of Tsukuba

関連論文

• Hausdorff hyperspaces of R-m and their dense subspaces
• The completions of metric ANR's and homotopy dense subsets
• Hyperspaces with the Hausdorff Metric and Uniform ANR's
• Small subdivisions of simplicial complexes with the metric topology
• On topologies of triangulated infinite-dimensional manifolds
• The completions of metric ANR's and homotopy dense subsets

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