Disjoint sequences in Boolean algebras

Ján Jakubík

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 4, page 411-418
  • ISSN: 0862-7959

Abstract

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We deal with the system Conv B of all sequential convergences on a Boolean algebra B . We prove that if α is a sequential convergence on B which is generated by a set of disjoint sequences and if β is any element of Conv B , then the join α ∨ β exists in the partially ordered set Conv B . Further we show that each interval of Conv B is a Brouwerian lattice.

How to cite

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Jakubík, Ján. "Disjoint sequences in Boolean algebras." Mathematica Bohemica 123.4 (1998): 411-418. <http://eudml.org/doc/248291>.

@article{Jakubík1998,
abstract = {We deal with the system $\{\operatorname\{Conv\}\} B$ of all sequential convergences on a Boolean algebra $B$. We prove that if $\alpha $ is a sequential convergence on $B$ which is generated by a set of disjoint sequences and if $\beta $ is any element of $\{\operatorname\{Conv\}\} B$, then the join $\alpha \vee \beta $ exists in the partially ordered set $\{\operatorname\{Conv\}\} B$. Further we show that each interval of $\{\operatorname\{Conv\}\} B$ is a Brouwerian lattice.},
author = {Jakubík, Ján},
journal = {Mathematica Bohemica},
keywords = {Boolean algebra; sequential convergence; disjoint sequence; Brouwerian lattice; Boolean algebra; sequential convergence; disjoint sequence; Brouwerian lattice},
language = {eng},
number = {4},
pages = {411-418},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Disjoint sequences in Boolean algebras},
url = {http://eudml.org/doc/248291},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Jakubík, Ján
TI - Disjoint sequences in Boolean algebras
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 4
SP - 411
EP - 418
AB - We deal with the system ${\operatorname{Conv}} B$ of all sequential convergences on a Boolean algebra $B$. We prove that if $\alpha $ is a sequential convergence on $B$ which is generated by a set of disjoint sequences and if $\beta $ is any element of ${\operatorname{Conv}} B$, then the join $\alpha \vee \beta $ exists in the partially ordered set ${\operatorname{Conv}} B$. Further we show that each interval of ${\operatorname{Conv}} B$ is a Brouwerian lattice.
LA - eng
KW - Boolean algebra; sequential convergence; disjoint sequence; Brouwerian lattice; Boolean algebra; sequential convergence; disjoint sequence; Brouwerian lattice
UR - http://eudml.org/doc/248291
ER -

References

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  1. J. Jakubík, Sequential convergences in Boolean algebras, Czechoslovak Math. J. 38 (1988), 520-530. (1988) MR0950306
  2. J. Jakubík, Convergences and higher degrees of distributivity of lattice ordered groups and of Boolean algebras, Czechoslovak Math. J. 40 (1990), 453-458. (1990) MR1065024
  3. H. Löwig, 10.2307/1970464, Ann. Math. 13 (1941), 1138-1196. (1941) MR0006494DOI10.2307/1970464
  4. J. Novák M. Novotný, On the convergence in σ -algebras of point-sets, Czechoslovak Math. J. 3 (1953), 291-296. (1953) MR0060572
  5. F. Papangelou, 10.1007/BF01344076, Math. Ann. 155 (1964), 81-107. (1964) Zbl0131.02601MR0174498DOI10.1007/BF01344076

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