Outer measure analysis of topological lattice properties
type: Item
instance of: scholarly article
title: Outer measure analysis of topological lattice properties
zbMATH Open document ID: 0883.28012
DOI: 10.1155/S0161171297000380
author: Setiawati Wibisono
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1998-03-22T00:00:00Z
full work available at URL: https://eudml.org/doc/47825
review text: Summary: Let \(X\) be a set and \(\mathcal L\) a lattice of subsets of \(X\) such that \(\emptyset, X\in{\mathcal L}\). \({\mathcal A}({\mathcal L})\) is the algebra generated by \(\mathcal L\); \(M({\mathcal L})\) the set of nontrivial, finite, nonnegative, finitely additive measures on \({\mathcal A}({\mathcal L})\); and \(I({\mathcal L})\) those elements of \(M({\mathcal L})\) which just take the values zero and one. Various subsets of \(M({\mathcal L})\) and \(I({\mathcal L})\) are included which display smoothness and regularity properties. We consider several outer measures associated with elements of \(M({\mathcal L})\) and relate their behavior to smoothness and regularity conditions as well as to various lattice topological properties. In addition, their measurable sets are fully investigated. In the case of two lattices \({\mathcal L}_1\), \({\mathcal L}_2\) with \({\mathcal L}_1\subset{\mathcal L}_2\), we present consequences of separation properties between the pair of lattices in terms of these outer measures, and further demonstrate the extension of smoothness conditions on \({\mathcal L}_1\) to \({\mathcal L}_2\).
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 28A60
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 06B30
zbMATH DE Number: 1046336
zbMATH Keywords: countably compact
zbMATH Keywords: countably paracompact
zbMATH Keywords: semi-separation
zbMATH Keywords: separation
zbMATH Keywords: coseparation
zbMATH Keywords: outer measures
zbMATH Keywords: smoothness
zbMATH Keywords: regularity
zbMATH Keywords: lattices
MaRDI profile type: Publication
OpenAlex ID: W2120366222
description: scientific article; zbMATH DE number 1046336