Publisher Summary This chapter provides several definitions and theorems related to the Boolean algebra. The Boolean algebras that can be particularly useful are based on topological spaces. One requires the notion of regular open set, which receives relatively little attention in texts on topological spaces. However, the total information required about topological spaces is very little indeed. Not every Boolean algebra is complete. A Boolean algebra A is said to satisfy the countable chain condition if every disjoint set of nonzero elements of A is countable.