For every Hausdorff space \(Y\) there exists a non-trivial Moore space on which all continuous functions into \(Y\) are constant
type: Item
instance of: scholarly article
title: For every Hausdorff space \(Y\) there exists a non-trivial Moore space on which all continuous functions into \(Y\) are constant
zbMATH Open document ID: 0538.54016
author: Harald Brandenburg
author: Adam Mysior
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In an early version of a recent survey article on categorical topology, H. Herrlich raised the question whether there exists a Moore space \(Y\) such that every Moore space can be embedded into some topological power of \(Y\). We answer this question by proving the result mentioned in the title, which shows that there does not exist any Hausdorff space \(Y\) with the property that every Moore space can be embedded into some power of \(Y\). Additionally, a simple proof is given of the theorem of H. Herrlich and A. Ramer that for every \(T_ 1\)-space \(X\) there exists a regular space \(S\) containing two distinct points \(a, b\) such that \(f(a)=f(b)\) for every continuous mapping from \(S\) into \(X\).
Mathematics Subject Classification ID: 54E30
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 3855968
zbMATH Keywords: metacompact Moore space
zbMATH Keywords: no universal Moore space
MaRDI profile type: Publication
full work available at URL: pjm.1984.111.1
OpenAlex ID: W2055627641
DOI: 10.2140/PJM.1984.111.1
description: scientific article; zbMATH DE number 3855968