Further characterizations of boundedly UC spaces

Ľubica Holá; Dušan Holý

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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.