Nonshrinkable ''cell-like'' decompositons of s
Fine homotopy equivalences from s onto complete separable AR's are constructed that are analogs of certain cell-like maps defined on Euclidean space. In particular, (i) there is a fine homotpy equivalence f from s onto a complete separable AR X such that the collection of nondegenerate values \(N_ f\) of f is a singleton whose pre-image under f is a 1-dimensional AR wildly embedded in s, and (ii) there is a fine homotopy equivalence g from s onto a complete separable AR Y such that \(N_ g\) is a Cantor set and every nondegenerate fiber of g is a tame Z-set in s. Neither X nor Y is homeomorphic to s but both become homeomorphic to s upon multiplication by a certain complete 1-dimensional AR.
scientific article; zbMATH DE number 3901654