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The sequential topology on complete Boolean algebras

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Główczyński W., Balcar B., Jech T. J.

Fundamenta Mathematicae

1998

tom 155

nr 1

59-78

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Balcar B.

1 Główczyński W.

1 Jech T. J.

1 1998

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The sequential topology on complete Boolean algebras