Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces
type: Item
instance of: scholarly article
title: Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces
zbMATH Open document ID: 1007.54029
DOI: 10.1016/S0166-8641(01)00082-7
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: The authors extend the result that every noncompact second countable regular space has a weaker Hausdorff connected topology. To this end they first prove that any metrizable noncompact space has a weaker metrizable nowhere locally compact topology. As a consequence they conclude that any metrizable noncompact space has a weaker Hausdorff connected topology. Finally they establish that the same holds for any Hausdorff space \(X\) with a \(\sigma\)-locally finite base whose weight \(w(X)\) is a successor cardinal. Many interesting questions related to these results are asked.
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54C05
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54E45
zbMATH DE Number: 1787504
zbMATH Keywords: metrizable space
zbMATH Keywords: nowhere locally compact space
zbMATH Keywords: connected space
zbMATH Keywords: condensation
author: Gary Gruenhage
author: Vladimir Tkachuk
author: Richard G. Wilson
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787504