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The sequential topology on complete Boolean algebras

Wiesław Główczyński, Bohuslav Balcar, Thomas Jech (1998)

Fundamenta Mathematicae

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.

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