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The sequential topology on complete Boolean algebras

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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.
  • Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Mathematical Institute of the Academy of Sciences of Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
  • Department of Mathematics, The Pennsylvania State University, 218 McAllister Bldg., University Park, Pennsylvania 16802, U.S.A.
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