Complete metric absolute neighborhood retracts
type: Item
instance of: scholarly article
title: Complete metric absolute neighborhood retracts
zbMATH Open document ID: 1028.54020
DOI: 10.1016/S0166-8641(03)00031-2
author: Wiesław Kubiś
published in: Topology and its Applications
publication date: 2003-09-04T00:00:00Z
review text: Two metric properties (B) and (B*) are introduced. It is shown that every complete metric space with Property (B) is an absolute neighborhood retract, and a complete metric space with Property (B*) is an absolute retract. Some applications are obtained, for example it is proved that a compact metric space with a convex and locally convex simplicial structure is an AR, and the hyperspace of closed subsets of a separable Banach space endowed with the Wijsman topology is an AR.
Mathematics Subject Classification ID: 54C55
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 1974776
zbMATH Keywords: absolute (neighborhood) retract
zbMATH Keywords: complete metric space
zbMATH Keywords: polytope
zbMATH Keywords: Wijsman topology
reviewed by: Shou Lin
MaRDI profile type: Publication
cites work: Q4277838
cites work: Hyperspaces of finite subsets which are homeomorphic to \(\aleph _ 0\)- dimensional linear metric spaces
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cites work: Q3264660
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cites work: Investigating the ANR-property of metric spaces
cites work: Hyperspaces of non-compact metrizable spaces which are homeomorphic to the Hilbert cube.
full work available at URL: s0166-8641(03)00031-2
OpenAlex ID: W2140037137
description: scientific article; zbMATH DE number 1974776