Lattice-valued convergence spaces and regularity
type: Item
instance of: scholarly article
title: Lattice-valued convergence spaces and regularity
zbMATH Open document ID: 1177.54003
author: G. Jäger
published in: Fuzzy Sets and Systems
publication date: 2009-08-28T00:00:00Z
review text: The author continues his previous studies on lattice-valued convergence spaces. The main purpose of this paper is to use some duality conditions in order to characterize regularity of such spaces with the lattice in the form of a complete Heyting algebra. Moreover some separation axioms are introduced and they are used to prove some theorems on the regularity preservation. Yet another result derived in the paper is given by an extension theorem for continuous mappings from a dense subspace to a regular space. The regularity axiom presented in the paper is also characterized in the restricted lattice context of complete Boolean algebras.
reviewed by: Andrzej Świerniak
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54C05
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 5599471
zbMATH Keywords: \(L\)-fuzzy convergence
zbMATH Keywords: \(L\)-topology
zbMATH Keywords: \(L\)-filter
zbMATH Keywords: \(L\)-diagonal filter
zbMATH Keywords: \(L\)-convergence space
zbMATH Keywords: pretopological space
zbMATH Keywords: diagonal condition
zbMATH Keywords: regularity
zbMATH Keywords: T1-axiom
zbMATH Keywords: T2-axiom
zbMATH Keywords: dense subset
zbMATH Keywords: continuous extension
MaRDI profile type: Publication
full work available at URL: j.fss.2008.05.014
OpenAlex ID: W1988081158
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DOI: 10.1016/J.FSS.2008.05.014
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description: scientific article; zbMATH DE number 5599471