International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2565-2573
On compactness of lattices
Department of Mathematics, Pace University, Pleasantville 10570, NY, USA
Received 13 July 2004; Revised 27 June 2005
Copyright © 2005 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 set and a lattice of
subsets of . We denote by the set of those zero-one-valued nontrivial, finitely additive
measures on , the algebra generated by
, and we introduce other subsets of
. We study compactness/normality
properties either relating to a single lattice or relating
to a pair of lattices of subsets of .