Ultrametrics and infinite dimensional Whitehead theorems in shape theory
type: Item
instance of: scholarly article
title: Ultrametrics and infinite dimensional Whitehead theorems in shape theory
zbMATH Open document ID: 0855.54022
DOI: 10.1007/BF02567521
published in: Manuscripta Mathematica
publication date: 1996-04-28T00:00:00Z
full work available at URL: https://eudml.org/doc/156166
review text: The authors use a Cantor completion process to construct a complete non-Archimedean metric on the set of shape morphisms between pointed metric compacta. In the case of shape groups this produces a complete left and right invariant ultrametric on the group. This construction is analogous to the one used by the authors for the space of shape morphisms of nonpointed compacta [Shape as a Cantor completion process, Math. Z. (to appear)]. In applying this construction to pointed compacta, the authors obtain the norm on the shape groups mentioned above. This norm is used to prove a variety of known Whitehead type theorems in shape theory as well as some new results.
reviewed by: J. Keesling
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 54J05
zbMATH DE Number: 871038
zbMATH Keywords: pointed shape theory
zbMATH Keywords: Whitehead theorem
zbMATH Keywords: shape morphism
zbMATH Keywords: Cantor completion process
zbMATH Keywords: invariant ultrametric
zbMATH Keywords: shape theory
author: Manuel A. Morón
author: Francisco R. Ruiz del Portal
MaRDI profile type: Publication
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OpenAlex ID: W2028431020
description: scientific article; zbMATH DE number 871038