Factorwise rigidity of products of pseudo-arcs
type: Item
instance of: scholarly article
title: Factorwise rigidity of products of pseudo-arcs
zbMATH Open document ID: 0607.54023
DOI: 10.1016/0166-8641(86)90062-3
author: David J. Bellamy
author: Judy Kennedy
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: If \(X=\prod_{\gamma \in \Gamma}X_{\gamma}\) and H is a homeomorphism on X such that there exist a one-to-one map \(\phi\) of \(\Gamma\) onto \(\Gamma\) and for each \(\gamma\) in \(\Gamma\) a homeomorphism \(h_{\gamma}\) of \(X_{\gamma}\) onto \(X_{\phi (\gamma)}\) such that \(H(x)_{\phi (\gamma)}=h_{\gamma}(x_{\gamma})\) for each x in X, then H is said to be factor preserving. If every homeomorphism on X is factor preserving, then X is said to be factorwise rigid. It is proved that every product of pseudoarcs is factorwise rigid. The proof involves many known properties of the pseudoarc, including homogeneity. The authors ask whether every product of hereditarily indecomposable continua is factorwise rigid.
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 3982046
zbMATH Keywords: factor preserving product
zbMATH Keywords: product continuum
zbMATH Keywords: homeomorphism
zbMATH Keywords: homogeneous continuum
zbMATH Keywords: \(\epsilon \)-mapping
zbMATH Keywords: pseudoarc
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90062-3
OpenAlex ID: W2095468344
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description: scientific article; zbMATH DE number 3982046