International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 25-32
doi:10.1155/S0161171298000039

On lattice-topological properties of general Wallman spaces

Abstract

Let X be an arbitrary set and ℒ a lattice of subsets of X such that ϕ,X∈ℒ.𝒜(ℒ) is the algebra generated by ℒ and I(ℒ) consists of all zero-one valued finitely additive measures on 𝒜(ℒ). Various subsets of and I(ℒ) are considered and certain lattices are investigated as well as the topology of closed sets generated by them. The lattices are investigated for normality, regularity, repleteness and completeness. The topologies are similarly discussed for various properties such as T2 and Lindelöf.