Convergence-theoretic approach to quotient quest
type: Item
instance of: scholarly article
title: Convergence-theoretic approach to quotient quest
zbMATH Open document ID: 0862.54001
DOI: 10.1016/0166-8641(96)00067-3
author: Szymon Dolecki
published in: Topology and its Applications
publication date: 1997-05-25T00:00:00Z
review text: In topology there are natural relations between various classes of maps on one hand and various properties of topological spaces on the other hand. In particular there are theorems of the following kind: a topological space \(X\) has property \(P\) iff there exists a space \(Y\) with (the usually nicer) property \(Q\) and a special kind of quotient maps \(f:Y\to X\) (e.g., hereditary quotient, bi-quotient, almost open, open). The author investigates corresponding questions in the setting of convergence spaces and provides many interesting results. These generalizations seem particularly appropriate in view of the fact special types of quotient maps in Top are nothing else but categorical quotient maps in categories of suitable convergence spaces [cf. in particular \textit{H. L. Bentley}, the reviewer and \textit{R. Lowen}, Res. Expo. Math. 18, 3-20 (1991; Zbl 0753.18002)].
reviewed by: Horst Herrlich
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54B15
zbMATH DE Number: 943248
zbMATH Keywords: pretopology
zbMATH Keywords: pseudotopology
zbMATH Keywords: hereditary quotient
zbMATH Keywords: bi-quotient
zbMATH Keywords: almost open
zbMATH Keywords: convergence spaces
zbMATH Keywords: categorical quotient maps
MaRDI profile type: Publication
full work available at URL: 0166-8641(96)00067-3
OpenAlex ID: W2054584585
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description: scientific article; zbMATH DE number 943248