# Disjoint sequences in Boolean algebras

Mathematica Bohemica (1998)

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

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topJakubík, 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

top- J. Jakubík, Sequential convergences in Boolean algebras, Czechoslovak Math. J. 38 (1988), 520-530. (1988) MR0950306
- 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
- H. Löwig, 10.2307/1970464, Ann. Math. 13 (1941), 1138-1196. (1941) MR0006494DOI10.2307/1970464
- J. Novák M. Novotný, On the convergence in $\sigma $-algebras of point-sets, Czechoslovak Math. J. 3 (1953), 291-296. (1953) MR0060572
- F. Papangelou, 10.1007/BF01344076, Math. Ann. 155 (1964), 81-107. (1964) Zbl0131.02601MR0174498DOI10.1007/BF01344076

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