Normal lattices and coseparation of lattices
Barry B. Mittag · International Journal of Mathematics and Mathematical Sciences · 1997
Let X be an arbitrary non‐empty set, and let ℒ be a lattice of subsets of X such that ∅, X ∈ ℒ. We first summarize a number of known conditions which are equivalent to ℒ being normal. We then develop new equivalent conditions in terms of set functions associated with μ ∈ I(ℒ), the set of all non‐trivial, zero‐one valued finitely additive measures on the algebra generated‐by ℒ′. We finally generalize all the above to the situation where ℒ1 and ℒ2 are a pair of lattices of subsets of X with , and where we obtain equivalent conditions for ℒ1 to coseparate ℒ2.