The sequential topology on complete Boolean algebras

Wiesław Główczyński; Bohuslav Balcar; Thomas Jech

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 1, page 59-78
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Główczyński, Wiesław, Balcar, Bohuslav, and Jech, Thomas. "The sequential topology on complete Boolean algebras." Fundamenta Mathematicae 155.1 (1998): 59-78. <http://eudml.org/doc/212243>.

@article{Główczyński1998,
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.},
author = {Główczyński, Wiesław, Balcar, Bohuslav, Jech, Thomas},
journal = {Fundamenta Mathematicae},
keywords = {complete Boolean algebra; sequential topology; Maharam submeasure; sequential cardinal; Maharam submeasures},
language = {eng},
number = {1},
pages = {59-78},
title = {The sequential topology on complete Boolean algebras},
url = {http://eudml.org/doc/212243},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Główczyński, Wiesław
AU - Balcar, Bohuslav
AU - Jech, Thomas
TI - The sequential topology on complete Boolean algebras
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 1
SP - 59
EP - 78
AB - 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.
LA - eng
KW - complete Boolean algebra; sequential topology; Maharam submeasure; sequential cardinal; Maharam submeasures
UR - http://eudml.org/doc/212243
ER -

References

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