The completions of metric ANR's and homotopy dense subsets

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概要

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• In this paper, considering the problem when the completion of a metric ANR X is an ANR and X is homotopy dense in the completion, we give some sufficient conditions. It is also shown that each uniform ANR is homotopy dense in any metric space containing X isometrically as a dense subset, and that a metric space X is a uniform ANR if and only if the metric completion of X is a uniform ANR with X a homotopy dense subset. Furthermore, introducing the notions of densely (local) hyper-connectedness and uniformly (local) hyper-connectedness, we characterize of AR's (ANR's) and uniform AR's (uniform ANR's), respectively.

• 一般社団法人 日本数学会の論文

著者

• Sakai Katsuro

  Institute Of Mathematics University Of Tsukuba

関連論文

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• The completions of metric ANR's and homotopy dense subsets

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