Generalized stable shape and the Whitehead theorem
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.
stable shape category for arbitrary spaces
scientific article; zbMATH DE number 763545
scientific article