Dimensionally valuable cell-like resolution for \(ANR\)-compacta
type: Item
instance of: scholarly article
title: Dimensionally valuable cell-like resolution for \(ANR\)-compacta
zbMATH Open document ID: 0809.54013
author: V. L. Sukhikh
published in: Moscow University Mathematics Bulletin
publication date: 1994-04-06T00:00:00Z
review text: It is shown that every ANR-compactum \(X\) has a cell-like resolution \(f: Y\to X\) by means of the ANR-compactum \(Y\) of dimension \(\dim Y=\dim X\) with Borsuk condition \((\Delta)\). The condition \((\Delta)\) on \(Y\) means the local contractibility of \(Y\) with the additional requirement that every small \(k\)-dimensional subset \(A\subset Y\) is contractible to a point in a small \((k+1)\)-dimensional subset \(B\subset Y\). Now it is known that there are ANR-compacta for which the Borsuk condition \((\Delta)\) does not hold.
Mathematics Subject Classification ID: 54C55
zbMATH DE Number: 486801
zbMATH Keywords: cell-like map
zbMATH Keywords: ANR-compactum
zbMATH Keywords: cell-like resolution
zbMATH Keywords: dimension
zbMATH Keywords: Borsuk condition
reviewed by: Alexander Dranishnikov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 486801