Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 52, Number 4 (2000), 835-846.
The completions of metric ANR's and homotopy dense subsets
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.
J. Math. Soc. Japan, Volume 52, Number 4 (2000), 835-846.
First available in Project Euclid: 10 June 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57N20: Topology of infinite-dimensional manifolds [See also 58Bxx] 58D05: Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05] 46E15: Banach spaces of continuous, differentiable or analytic functions
SAKAI, Katsuro. The completions of metric ANR's and homotopy dense subsets. J. Math. Soc. Japan 52 (2000), no. 4, 835--846. doi:10.2969/jmsj/05240835. https://projecteuclid.org/euclid.jmsj/1213107112