| Title:
|
Disjoint sequences in Boolean algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
411-418 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Boolean algebra |
| Keyword:
|
sequential convergence |
| Keyword:
|
disjoint sequence |
| Keyword:
|
Brouwerian lattice |
| MSC:
|
06A12 |
| MSC:
|
06E05 |
| MSC:
|
06E99 |
| MSC:
|
11B99 |
| idZBL:
|
Zbl 0934.06017 |
| idMR:
|
MR1667113 |
| DOI:
|
10.21136/MB.1998.125963 |
| . |
| Date available:
|
2009-09-24T21:33:46Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125963 |
| . |
| Reference:
|
[1] J. Jakubík: Sequential convergences in Boolean algebras.Czechoslovak Math. J. 38 (1988), 520-530. MR 0950306 |
| Reference:
|
[2] J. Jakubík: Convergences and higher degrees of distributivity of lattice ordered groups and of Boolean algebras.Czechoslovak Math. J. 40 (1990), 453-458. MR 1065024 |
| Reference:
|
[3] H. Löwig: Intrinsic topology and completion of Boolean rings.Ann. Math. 13 (1941), 1138-1196. MR 0006494, 10.2307/1970464 |
| Reference:
|
[4] J. Novák M. Novotný: On the convergence in $\sigma$-algebras of point-sets.Czechoslovak Math. J. 3 (1953), 291-296. MR 0060572 |
| Reference:
|
[5] F. Papangelou: Order convergence and topological completion of commutative lattice-groups.Math. Ann. 155 (1964), 81-107. Zbl 0131.02601, MR 0174498, 10.1007/BF01344076 |
| . |
