On generalized neighbourhood systems
type: Item
instance of: scholarly article
title: On generalized neighbourhood systems
zbMATH Open document ID: 1199.54002
published in: Acta Mathematica Hungarica
publication date: 2009-12-28T00:00:00Z
review text: Let \(X\) be a nonempty set. A generalized topology (GT) \(\mu\) on \(X\) is a subset of \(\exp X\) such that \(\emptyset \in \mu\) and every union of elements of \(\mu\) belongs to \(\mu\). A map \(\psi : X \rightarrow \exp X\) is called a generalized neighbourhood system (GNS) on \(X\) if, for \(x \in X\) and \(V\in \psi (x)\), we have \(x\in V\). Moreover, in this paper, two operations \(\iota_{\psi}\) and \(\gamma_{\psi}\) are defined: for \(A\subset X\), \(x\in \iota_{\psi}(A)\) iff there is \(V\in \psi (x)\) such that \(V\subset A\); \(x\in \gamma_{\psi}(A)\) iff \(V\in \psi (x)\) implies \(V\cap A\neq \emptyset\). In this paper, the author considers problems connected with generating a GT by a GNS and the operations \(\iota_{\psi}\) and \(\gamma_{\psi}\). The paper is finished by short considerations connected with \((\phi ,\psi )\)-continuity.
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 5651859
zbMATH Keywords: continuous maps
author: Ákos Császár
reviewed by: Ryszard Pawlak
MaRDI profile type: Publication
full work available at URL: s10474-008-7224-5
OpenAlex ID: W2122385619
cites work: Generalized topology, generalized continuity
cites work: Generalized open sets in generalized topologies
cites work: On weak neighborhood systems and spaces
DOI: 10.1007/S10474-008-7224-5
description: scientific article; zbMATH DE number 5651859