Epimorphisms and cowellpoweredness for separated metrically generated theories
type: Item
instance of: scholarly article
title: Epimorphisms and cowellpoweredness for separated metrically generated theories
zbMATH Open document ID: 1121.54023
author: Eva Colebunders
author: A. Gerlo
author: V. Claes
published in: Acta Mathematica Hungarica
publication date: 2007-05-08T00:00:00Z
review text: The paper presents new results about metrically generated theories, compare \textit{E. Colebunders} and \textit{R. Lowen} [Proc. Am. Math. Soc. 133, 1547--1556 (2005; Zbl 1073.54006)]). For metrically generated constructs \(\mathbb X\) the authors give an internal characterization of the regular closure operator on \(\mathbb X,\) determined by the subconstruct \(\mathbb X_0\), consisting of its \(T_0\) objects. That result is then used to describe the epimorphisms in \(\mathbb X_0\) and to prove that all constructs of that type are cowellpowered. The methods lead to some new results (for instance a characterization of the epis in \(\mathbb A\mathbb P_0\), where \(\mathbb A\mathbb P\) denotes the construct of approach spaces), besides unifying many known cases.
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18B99
zbMATH DE Number: 5150257
zbMATH Keywords: topological construct
zbMATH Keywords: metrically generated theory
zbMATH Keywords: \(T_0\) object
zbMATH Keywords: epimorphism
zbMATH Keywords: cowellpoweredness
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: s10474-006-0518-6
OpenAlex ID: W2004470041
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DOI: 10.1007/S10474-006-0518-6
description: scientific article; zbMATH DE number 5150257