The sequential topology on complete Boolean algebras
Tom 155 / 1998
Fundamenta Mathematicae 155 (1998), 59-78
DOI: 10.4064/fm-155-1-59-78
Streszczenie
We investigate the sequential topology $τ_{s}$ 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 $(B,τ_{s})$ is Hausdorff. We also characterize sequential cardinals.
