The sequential topology on complete Boolean algebras

Abstract

We investigate the sequential topology ${\tau }_s$ on a complete Boolean algebra $B$ determined by algebraically convergent sequences in $B$. We show the role of weak distributivity of $B$ in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for $B$ to carry a strictly positive Maharam submeasure is that $B$ is ccc and that the space $(B,{\tau }_s)$ is Hausdorff. We also characterize sequential cardinals.