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.