The sequential topology on complete Boolean algebras

Volume 155 / 1998

Bohuslav Balcar, Wiesław Główczyński, Thomas Jech Fundamenta Mathematicae 155 (1998), 59-78 DOI: 10.4064/fm-155-1-59-78

Abstract

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.

Authors

  • Bohuslav Balcar
  • Wiesław Główczyński
  • Thomas Jech

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