Lattice Operators and Topologies

Table 1

Summary of notation.

ℬ	Complete Boolean algebra with zero (𝟎) and unit (𝐞)
ℒ,ℒ𝑛	Lattices with 𝟎 and 𝐞
𝐹,𝐹𝑛,𝐺,𝐻	Filters without 𝟎
𝒜(ℒ)	The Algebra generated by ℒ
𝜇,𝜇𝑓	Finitely additive zero-one measures on ℬ
𝜏(ℒ)	Closed elements of ℬ
ℳ	Meet semi-lattice
𝒫(𝑆)	Power set of the set 𝑆