The sequential topology on complete Boolean algebras

Details The sequential topology on complete Boolean algebras The sequential topology on complete Boolean algebras

1996-12-03

arxiv.org/abs/math/9612207v1

Mathematics

Logic

Scientific paper

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.

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