Normal characterizations of lattices
type: Item
instance of: scholarly article
title: Normal characterizations of lattices
zbMATH Open document ID: 0995.28001
DOI: 10.1155/S0161171201007256
author: Carmen Vlad
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49427
full work available at URL: S0161171201007256.html
review text: Summary: Let \(\mathbf{X}\) be an arbitrary nonempty set and \(\mathcal{L}\) a lattice of subsets of \(\mathbf{X}\) such that \(\emptyset\), \(\mathbf{X} \in \mathcal{L}\). Let \(\mathcal{A(L)}\) denote the algebra generated by \(\mathcal{L}\) and \(\mathbf{I} (\mathcal{L})\) denote those nontrivial, zero-one valued, finitely additive measures on \(\mathcal{A(L)}\). We discuss some of the normal characterizations of lattices in terms of the associated lattice regular measures, filters and outer measures. We consider the interplay between normal lattices, regularity or \(\sigma\)-smoothness properties of measures, lattice topological properties and filter correspondence. Finally, we start a study of slightly, mildly and strongly normal lattices and express then some of these results in terms of the generalized Wallman spaces.
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 06B30
zbMATH DE Number: 1780296
zbMATH Keywords: finitely additive measures
zbMATH Keywords: lattice regular measures
zbMATH Keywords: outer measures
zbMATH Keywords: regularity
zbMATH Keywords: filter correspondence
zbMATH Keywords: strongly normal lattices
zbMATH Keywords: generalized Wallman spaces
MaRDI profile type: Publication
OpenAlex ID: W2044817856
description: scientific article; zbMATH DE number 1780296