International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 10, Pages 561-570
Normal characterizations of lattices
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 be an arbitrary nonempty set and a lattice of subsets of such that , . Let denote the algebra generated by and denote those nontrivial, zero-one valued, finitely additive
measures on . 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 -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.