Regularity of the category of Kelley spaces
type: Item
instance of: scholarly article
title: Regularity of the category of Kelley spaces
zbMATH Open document ID: 0840.18002
DOI: 10.1007/BF00872904
published in: Applied Categorical Structures
publication date: 1996-07-01T00:00:00Z
review text: It is well known that, although the category of all topological spaces has image factorizations, it fails to be regular because quotient maps are not stable under pullback. In this short note, the authors prove that the category of Hausdorff \(k\)-spaces is regular, by an ingenious argument making use of its Cartesian closedness.
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54D50
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 18A32
zbMATH DE Number: 854352
zbMATH Keywords: regularity
zbMATH Keywords: Kelley spaces
zbMATH Keywords: category of topological spaces
zbMATH Keywords: category of Hausdorff \(k\)-spaces
zbMATH Keywords: stable under pullback
zbMATH Keywords: Cartesian closedness
author: Francesca Cagliari
author: Sandra Mantovani
author: E. M. Vitale
reviewed by: Peter Johnstone
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00872904
OpenAlex ID: W2071371673
description: scientific article; zbMATH DE number 854352