Atomless Boolean algebra

Summary

An atomless Boolean algebra is a Boolean algebra with no atoms: below every nonzero element there is a strictly smaller nonzero element. One example is the algebra of clopen subsets of the Cantor space. Others are the free Boolean algebra on infinitely many generators and the regular open algebra of $\R$. Any two countable atomless Boolean algebras with $0 \ne 1$ are isomorphic, so there is essentially one such algebra. Atomless algebras are the opposite extreme to the complete atomic Boolean algebras, which are power sets.