The pullback closure operator and generalisations of perfectness
type: Item
instance of: scholarly article
title: The pullback closure operator and generalisations of perfectness
zbMATH Open document ID: 0912.18001
DOI: 10.1007/BF00124119
author: David Holgate
published in: Applied Categorical Structures
publication date: 1997-11-06T00:00:00Z
review text: The author studies a closure operator \(\Phi_{(R,r)}\) [in the sense of \textit{E. Giuli} and \textit{D. Dikranyan}, Topology Appl. 27, 129-143 (1987; Zbl 0634.54008)] associated with a pointed endofunctor \((R,r)\), defined by means of pullback. In the case of a reflector of a topological category this was done by \textit{D. Dikranyan} [Suppl. Rend. Circ. Mat. Palermo, II. Ser. 29, 105-160 (1992; Zbl 0782.54009)]. The author offers the first systematic study of this closure operator in full generality and studies various notions of perfectness relative to the pointed endofunctor \({(R,r)}\) and its pullback closure operator \(\Phi_{(R,r)}\).
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18A32
zbMATH DE Number: 1053694
zbMATH Keywords: separation
zbMATH Keywords: closure operator
zbMATH Keywords: connectedness
reviewed by: Dikran Dikranjan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00124119
OpenAlex ID: W4242723513
description: scientific article; zbMATH DE number 1053694