Closed structures on categories of topological spaces
type: Item
instance of: scholarly article
title: Closed structures on categories of topological spaces
zbMATH Open document ID: 0568.54015
DOI: 10.1016/0166-8641(85)90078-1
author: Juraj Činčura
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: It is proved that any full epireflective subcategory of the category Top of topological spaces admits exactly one symmetric monoidal closed structure. In 1979, the author published this result in the case of Top itself [see Comment. Math. Univ. Carol. 20, 431-446 (1979; Zbl 0416.18014)] but following \textit{G. M. Kelly} and \textit{F. Rossi} [Bull. Aust. Math. Soc. 31, 41-59 (1985; Zbl 0548.18005)] the proof contains a gap. Independently of the paper under review, it was re-proved by \textit{M. C. Pedicchio} and \textit{S. Solimini} [On a ''good'' dense class of topological spaces, Quaderno n. 100, Univ. Trieste (1984)] and the author affirm that their method applies to a general epireflective subcategory, too.
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 18D15
zbMATH DE Number: 3907330
zbMATH Keywords: full epireflective subcategory
zbMATH Keywords: symmetric monoidal closed structure
reviewed by: Jiří Rosický
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90078-1
OpenAlex ID: W1986824257
cites work: Tensor Products and Bimorphisms
cites work: Q3205396
cites work: Q3852364
cites work: Q3964754
cites work: Q4052073
cites work: Q5586461
cites work: Q3954491
cites work: Topologische Reflexionen und Coreflexionen
cites work: Topological functors
cites work: Q5682456
cites work: Q5631740
cites work: Q5639839
cites work: Initially Structured Categories and Cartesian Closedness
cites work: Every topological category is convenient for Gelfand duality
description: scientific article; zbMATH DE number 3907330