Generalized stable shape and the Whitehead theorem
type: Item
instance of: scholarly article
title: Generalized stable shape and the Whitehead theorem
zbMATH Open document ID: 0831.55010
DOI: 10.1016/0166-8641(94)00082-E
author: Takahisa Miyata
author: Jack Segal
published in: Topology and its Applications
publication date: 1995-06-13T00:00:00Z
review text: The authors, using generalized expansions define the stable shape category for arbitrary spaces. Their definition is based on the category of CW-spectra. So this approach allows to work on cells of CW-spectra. They show that the stable shape category for compacta defined by Dold, Puppe, Henn embeds in this stable shape category. The authors prove a finite-dimensional version of a Whitehead type theorem for CW-spectra, then they generalize the statement for pro-CW-spectra. A notion of dimension in this stable shape category is defined. Finally they obtain a stable shape version of a Whitehead type theorem. The authors also give some examples which show that the condition of finite dimensionality in the Whitehead theorem cannot be omitted.
reviewed by: Corina Mohorianu
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 54B35
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 55Q10
zbMATH DE Number: 763545
zbMATH Keywords: stable shape category for arbitrary spaces
zbMATH Keywords: CW-spectra
zbMATH Keywords: Whitehead type theorem for CW-spectra
zbMATH Keywords: pro-CW-spectra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 763545