Coarser connected metrizable topologies
type: Item
instance of: scholarly article
title: Coarser connected metrizable topologies
zbMATH Open document ID: 1202.54018
author: Lynne Yengulalp
published in: Topology and its Applications
publication date: 2010-08-27T00:00:00Z
review text: The main result of this paper is that whenever \(\tau\) is a non-compact metrizable topology on a set \(X\) of weight at least \(\mathfrak c\), then there is a connected metrizable topology \(\mu\subseteq\tau\) on \(X\). It is known that if \(w(X)<\mathfrak c\), then no such connected regular topology \(\mu\) need exist. The principal theorem generalizes results of a) \textit{G. Gruenhage, V. V. Tkachuk} and the reviewer [Topology Appl. 120, No.~3, 365--384 (2002; Zbl 1007.54029)] who showed the existence of a connected Hausdorff topology \(\mu\subseteq\tau\); b) \textit{W. G. Fleissner, J. Porter} and \textit{J. Roitman} [Topology Appl. 142, No.~1--3, 131--157 (2004; Zbl 1068.54002)] who showed that such a metrizable topology \(\mu\) exists whenever \(\tau\) is zero-dimensional; and c) \textit{I. Druzhinina} [Houston J. Math. 30, No.~3, 751--766 (2004; Zbl 1059.54022)] who showed that such a metrizable topology \(\mu\) exists if the extent of \((X,\tau)\) is attained.
reviewed by: Richard G. Wilson
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 5775736
zbMATH Keywords: coarser connected topology
zbMATH Keywords: metrizable topology
zbMATH Keywords: weight at least continuum
zbMATH Keywords: extent not assumed
MaRDI profile type: Publication
full work available at URL: j.topol.2010.06.002
OpenAlex ID: W1983360097
cites work: Q4827102
cites work: Topological Completions of Metrizable Spaces
cites work: Coarser connected topologies
cites work: Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces
cites work: Q4383370
DOI: 10.1016/J.TOPOL.2010.06.002
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description: scientific article; zbMATH DE number 5775736