International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 10, Pages 561-570

Normal characterizations of lattices

Carmen D. Vlad

Department of Mathematics, Pace University, New York 10038, NY, USA

Received 30 March 2001

Copyright © 2001 Carmen D. Vlad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let X be an arbitrary nonempty set and a lattice of subsets of X such that , X. Let 𝒜() denote the algebra generated by and I() denote those nontrivial, zero-one valued, finitely additive measures on 𝒜(). In this paper, 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 σ-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.