English

The sequential topology on complete Boolean algebras

Logic 2016-09-06 v1

Abstract

We investigate the sequential topology τs\tau_s on a complete Boolean algebra BB determined by algebraically convergent sequences in BB. We show the role of weak distributivity of BB in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for BB to carry a strictly positive Maharam submeasure is that BB is ccc and that the space (B,τs)(B,\tau_s) is Hausdorff. We also characterize sequential cardinals.

Keywords

Cite

@article{arxiv.math/9612207,
  title  = {The sequential topology on complete Boolean algebras},
  author = {Bohuslav Balcar and Wieslaw Glowczynski and Thomas Jech},
  journal= {arXiv preprint arXiv:math/9612207},
  year   = {2016}
}