Coarser connected topologies
type: Item
instance of: scholarly article
title: Coarser connected topologies
zbMATH Open document ID: 1068.54002
author: William Fleissner
author: J. R. Porter
author: Judith Roitman
published in: Topology and its Applications
publication date: 2004-11-23T00:00:00Z
review text: This paper investigates topological spaces which have coarser connected topologies. If in a collectionwise normal space \(X\), the density equals the extent, which is attained and at least \(c\), then \(X\) has a coarser connected collectionwise normal topology. The authors point out that the separation property collectionwise normal can be replaced by other separation properties. A zero-dimensional metrizable space \(X\) of density at least \(c\) has a coarser connected metrizable topology. A non-\(H\)-closed Hausdorff space with a \(\sigma\)-locally finite base has a coarser connected Hausdorff topology. The authors give necessary and sufficient conditions for an ordinal to have a coarser connected Urysohn topology. In addition, the authors present a nowhere locally compact Hausdorff space \(X\) with no coarser connected Hausdorff topology, yet \(X\) is dense in a connected Hausdorff space \(Y\).
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 03E10
Mathematics Subject Classification ID: 54G05
zbMATH DE Number: 2117950
zbMATH Keywords: Coarser connected topology
zbMATH Keywords: Urysohn space
zbMATH Keywords: extent
zbMATH Keywords: metrizable
zbMATH Keywords: \(\sigma\)-locally finite base
zbMATH Keywords: \(\theta\)-continuous
zbMATH Keywords: ordinals
zbMATH Keywords: \(F\)-spaces
reviewed by: Maximilian Ganster
MaRDI profile type: Publication
full work available at URL: j.topol.2003.10.007
OpenAlex ID: W2010783896
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DOI: 10.1016/J.TOPOL.2003.10.007
description: scientific article; zbMATH DE number 2117950