Convergence-theoretic characterizations of compactness
type: Item
instance of: scholarly article
title: Convergence-theoretic characterizations of compactness
zbMATH Open document ID: 1022.54015
DOI: 10.1016/S0166-8641(01)00283-8
author: Szymon Dolecki
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: The author characterizes a variety of notions related to compactness in terms of concretely reflective convergence subcategories: topologies, paratopologies, hypotopologies and pseudotopologies. He also gives characterizations of hyperquotient maps (perfect, quasi-perfect, adherent and closed) and quotient maps (quotient, hereditarily quotient, countably bi-quotient, biquotient and almost open) in terms of various degrees of compactness of their fiber relations, and of sundry relaxations of inverse continuity. The results require too much notation to be describe here, but a good introduction to the theory and well arranged preliminaries are given.
reviewed by: Haruto Ohta
Mathematics Subject Classification ID: 54D60
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 1879134
zbMATH Keywords: compactness
zbMATH Keywords: convergence
zbMATH Keywords: pseudotopology
zbMATH Keywords: pretopology
zbMATH Keywords: quotient map
zbMATH Keywords: perfect map
zbMATH Keywords: compactoid filter
zbMATH Keywords: hyperquotient maps
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879134