ON LATTICE-TOPOLOGICAL PROPERTIES OF GENERAL WALLMAN SPACES

Let X be an arbitrary set and □ a lattice of subsets of X such that Ø,X ∈□. ..A(□) is the algebra generated by and I() consists of all zero-one valued finitely additive measures on A(□) Various subsets of I(□) 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 Lindelof