Ideal-valued topological structures
type: Item
instance of: scholarly article
title: Ideal-valued topological structures
zbMATH Open document ID: 1210.54012
author: Javier Gutiérrez García
author: Tomasz Kubiak
author: Alexander Šostak
published in: Fuzzy Sets and Systems
publication date: 2011-01-31T00:00:00Z
review text: With \(L\) a complete lattice and \(M\) a continuous lattice, this paper demonstrates an adjunction between \((L, M)\)- and \((L,\text{Idl}(M))\)-topological spaces; it is shown that the right adjoint functor provides a procedure of generating \((L, M)\)-topologies from antitone families of \((L, M)\)-topologies and how \((L,\text{Idl}(M))\)-topologies can be used to give an internal characterization of joins of \((L, M)\)-topologies. This paper is a sequel to the paper [\textit{T. Kubiak} and \textit{A. P. Šostak}, Quaest. Math. 20, No. 3, 423--429 (1997; Zbl 0890.54005)], where \(\text{Low}(M)\) with a completely distributive lattice \(M\) is used instead of \(\text{Idl}(M)\) (from the authors's abstract).
reviewed by: Bernhard Behrens
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 5843022
zbMATH Keywords: fuzzy topology
zbMATH Keywords: fuzzifying topology
zbMATH Keywords: continuous lattice
zbMATH Keywords: ideal
zbMATH Keywords: adjoint functor
zbMATH Keywords: principal ideal functor
zbMATH Keywords: sup functor
MaRDI profile type: Publication
full work available at URL: j.fss.2010.03.007
OpenAlex ID: W2003861009
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DOI: 10.1016/J.FSS.2010.03.007
description: scientific article; zbMATH DE number 5843022