The completions of metric ANR's and homotopy dense subsets
type: Item
instance of: scholarly article
title: The completions of metric ANR's and homotopy dense subsets
zbMATH Open document ID: 0974.57013
author: K. Sakai
published in: Journal of the Mathematical Society of Japan
publication date: 2001-05-03T00:00:00Z
review text: The author first gives some sufficient conditions when the completion \({\gamma}X\) of a metric ANR space \(X\) which is homotopy dense in \({\gamma}X\) is an ANR. He also shows that each uniform ANR is homotopy dense in any metric space in which it is contained 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. Finally, introducing the notions of densely (local) hyper-connectedness and uniformly (local) hyper-connectedness, he characterizes ANR's and uniform ANR's respectively.
reviewed by: Zvonko Čerin
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 55M15
zbMATH DE Number: 1553004
zbMATH Keywords: metric completion
zbMATH Keywords: homotopy dense
zbMATH Keywords: uniform ANR
zbMATH Keywords: densely locally hyper-connected
zbMATH Keywords: uniformly locally hyper-connected
zbMATH Keywords: absolute neighborhood retract
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05240835
OpenAlex ID: W2086812405
DOI: 10.2969/JMSJ/05240835
description: scientific article; zbMATH DE number 1553004