On a question of Mauldin and Ulam concerning homeomorphisms
type: Item
instance of: scholarly article
title: On a question of Mauldin and Ulam concerning homeomorphisms
zbMATH Open document ID: 1231.54010
author: Alessandro Fedeli
author: Attilio Le Donne
published in: Topology and its Applications
publication date: 2011-10-10T00:00:00Z
review text: Let \(E\), \(F\) be topological spaces. Given \(T:E\to F\), we say that \(T\) is an MU-map if, whenever \(A,B\subseteq E\) are homeomorphic then so are \(T(A), T(B)\subseteq F\). The following are the main results of the paper. Theorem. Let \(T:E\to F\) be a continuous onto MU-map. Then, \(T\) is a homeomorphism, provided one of the conditions below holds: i) \(F\) is weakly discretely generated (for each non-closed \(A\subseteq F\) there exists a discrete \(D\subseteq A\) such that \(\text{cl}(D)\setminus A\neq \emptyset\)), ii) \(E\) is a boundedly compact metric space and \(F\) is a Hausdorff space.
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 5956058
zbMATH Keywords: topological and metric space
zbMATH Keywords: homeomorphism
zbMATH Keywords: weakly discretely generated space
zbMATH Keywords: Hausdorff property
zbMATH Keywords: continuous onto map
MaRDI profile type: Publication
full work available at URL: j.topol.2011.06.055
OpenAlex ID: W2087072550
cites work: Q5610277
cites work: Q4720067
cites work: A course in metric geometry
cites work: Q3150238
cites work: Q3994935
cites work: Mathematical problems and games
DOI: 10.1016/J.TOPOL.2011.06.055
description: scientific article; zbMATH DE number 5956058