Abstract
In this paper, considering the problem when the completion of a metric ANR is an ANR and 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 isometrically as a dense subset, and that a metric space is a uniform ANR if and only if the metric completion of is a uniform ANR with 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.
Citation
Katsuro SAKAI. "The completions of metric ANR's and homotopy dense subsets." J. Math. Soc. Japan 52 (4) 835 - 846, October, 2000. https://doi.org/10.2969/jmsj/05240835
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