Topological Aspects of the Product of Lattices

Abstract

Let be an arbitrary nonempty set and a lattice of subsets of such that , . () denotes the algebra generated by , and () denotes those nonnegative, finite, finitely additive measures on (). In addition, () denotes the subset of () which consists of the nontrivial zero-one valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces, and products of a variety of measures.