A diagonal theorem for epireflective subcategories of Top and cowellpoweredness
type: Item
instance of: scholarly article
title: A diagonal theorem for epireflective subcategories of Top and cowellpoweredness
zbMATH Open document ID: 0617.54006
DOI: 10.1007/BF01790546
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: The authors investigate quotient-reflective subcategories of Top by means of suitable closure operators, introduced previously by Dikranjan and Giuli. For a class A of topological spaces, a subset of a topological space X is called A-closed in X provided it is closed in the topology having as subbase for the closed sets all equalizers of pairs of continuous maps from X into a space belonging to A. The two outstanding results are the following: (1) If A is quotient-reflective in Top, then a topological space X belongs to A if and only if the diagonal \(\Delta_ X\) is A-closed in \(X\times X\). (2) The quotient-reflective full subcategory Haus(Comp) of Top, consisting of those topological spaces X in which every compact subspace is Hausdorff, is not cowellpowered.
reviewed by: Horst Herrlich
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 4000952
zbMATH Keywords: cowellpoweredness
zbMATH Keywords: quotient-reflective subcategories
zbMATH Keywords: closure operators
Wikidata QID: Q115960153
author: Eraldo Giuli
author: M. Hušek
MaRDI profile type: Publication
cites work: Ordinal invariants for topological spaces
cites work: Q3736540
cites work: Q3715851
cites work: Bases of topological epi-reflections
cites work: Topologische Reflexionen und Coreflexionen
cites work: Q4069962
cites work: Q3877831
cites work: On weak Hausdorff spaces
cites work: Q4121154
cites work: Ordinal invariants in topology I. on two questions of Arhangel'skiǐ and Franklin
cites work: Q4147249
cites work: Q4114499
cites work: Semi-Hausdorff Spaces
cites work: Q4102451
cites work: Epi und extremer Mono in \(T_{2a}\)
cites work: The category of Urysohn spaces is not cowellpowered
cites work: Q3733748
full work available at URL: https://doi.org/10.1007/bf01790546
OpenAlex ID: W2092096481
description: scientific article; zbMATH DE number 4000952