A unified theory of generalized closed sets in weak structures
type: Item
instance of: scholarly article
title: A unified theory of generalized closed sets in weak structures
zbMATH Open document ID: 1274.54001
author: T. Noiri
author: A. Al-Omari
published in: Acta Mathematica Hungarica
publication date: 2013-04-05T00:00:00Z
review text: The authors continue the investigation of generalised topological spaces. Here it is no longer requested that the members of a generalised topology \(w\) are closed under intersection or union. In general, \(w\) does not replace the topology but is an additional structure added to a topology \(\tau\) on a set \(X\). For example the authors study when in a topological space \((X,\tau)\) the closed sets can be separated by disjoint \(w\)-open sets for a suitable weak structure \(w\). Prior work had considered special cases of \(w\), say the closures of open sets or the interiors of closed sets. The authors provide a large collection of results in various settings on the relation of normal closure in \((X,\tau)\) with generalised closure (induced by the weak structure) and so on.
reviewed by: Frank Stephan
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 6151033
zbMATH Keywords: weak structure
zbMATH Keywords: generalized closed set
zbMATH Keywords: generalized topology
zbMATH Keywords: minimal structure
zbMATH Keywords: \(w\)-regular
zbMATH Keywords: \(w\)-normal
zbMATH Keywords: topology with additional structure
MaRDI profile type: Publication
full work available at URL: s10474-011-0169-0
OpenAlex ID: W2073777092
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DOI: 10.1007/S10474-011-0169-0
description: scientific article; zbMATH DE number 6151033