Geodesic
The sequential topology on complete Boolean algebras
Fundamenta Mathematicae, Tome 155 (1998) no. 1, pp. 59-78

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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.
DOI : 10.4064/fm-155-1-59-78
Keywords: complete Boolean algebra, sequential topology, Maharam submeasure, sequential cardinal

Bohuslav Balcar 1 ; Wiesław Główczyński 1 ; Thomas Jech 1

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Bohuslav Balcar; Wiesław Główczyński; Thomas Jech. The sequential topology on complete Boolean algebras. Fundamenta Mathematicae, Tome 155 (1998) no. 1, pp. 59-78. doi: 10.4064/fm-155-1-59-78

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