Nonshrinkable ''cell-like'' decompositons of s
type: Item
instance of: scholarly article
title: Nonshrinkable ''cell-like'' decompositons of s
zbMATH Open document ID: 0565.57011
author: Philip L. Bowers
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 57N60
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 3901654
zbMATH Keywords: s-manifold
zbMATH Keywords: strong Z-set
zbMATH Keywords: Fine homotopy equivalences
zbMATH Keywords: cell-like maps
zbMATH Keywords: complete separable AR
zbMATH Keywords: nondegenerate values
zbMATH Keywords: tame Z-set
MaRDI profile type: Publication
full work available at URL: pjm.1986.124.257
OpenAlex ID: W2079238920
DOI: 10.2140/PJM.1986.124.257
description: scientific article; zbMATH DE number 3901654