Open Access
October, 2000 The completions of metric ANR's and homotopy dense subsets
Katsuro SAKAI
J. Math. Soc. Japan 52(4): 835-846 (October, 2000). DOI: 10.2969/jmsj/05240835


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.


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Katsuro SAKAI. "The completions of metric ANR's and homotopy dense subsets." J. Math. Soc. Japan 52 (4) 835 - 846, October, 2000.


Published: October, 2000
First available in Project Euclid: 10 June 2008

zbMATH: 0974.57013
MathSciNet: MR1774631
Digital Object Identifier: 10.2969/jmsj/05240835

Primary: ‎46E15 , ‎57N20‎ , 58D05

Keywords: ANR , densely locally hyper-connected , homotopy dense , the metric completion , uniform ANR , uniformly locally hyper-connected

Rights: Copyright © 2000 Mathematical Society of Japan

Vol.52 • No. 4 • October, 2000
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