# 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

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topGłówczyński, 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 -

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