Two remarks on weaker connected topologies
type: Item
instance of: scholarly article
zbMATH Open document ID: 0976.54019
publication date: 2001-12-17T00:00:00Z
full work available at URL: https://eudml.org/doc/121457
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54A35
zbMATH DE Number: 1682894
zbMATH Keywords: condensation
zbMATH Keywords: weaker connected topology
zbMATH Keywords: Luzin space
MaRDI profile type: Publication
author: P. Delaney
author: Winfried Just
title: Two remarks on weaker connected topologies
published in: Commentationes Mathematicae Universitatis Carolinae
review text: A topological space \((X,\mathcal T_0)\) condenses onto a space \((X,\mathcal T_1)\) if there is a topology \(\mathcal T_2\subset \mathcal T_0\) on \(X\) such that \((X,\mathcal T_2)\) and \((Y,\mathcal T_1)\) are homeomorphic. Under the assumption that the real line cannot be covered by \(\aleph_1\) nowhere dense sets, the authors prove that no discrete sum of \(\aleph_1\) zero-dimensional compact Hausdorff spaces of which at least two are nonempty condenses onto a connected Hausdorff space. This solves, in the negative, two problems formulated by \textit{M. G. Tkachenko, V. V. Tkachuk, V. V. Uspenskij} and \textit{R. G. Wilson} [Commentat. Math. Univ. Carol. 37, No. 4, 825-841 (1996; Zbl 0886.54034)].
reviewed by: Jaroslav Smítal
description: scientific article; zbMATH DE number 1682894