| Title:
|
Sequential convergences on generalized Boolean algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
1-14 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups. (English) |
| Keyword:
|
generalized Boolean algebra |
| Keyword:
|
abelian lattice ordered group |
| Keyword:
|
sequential convergence |
| Keyword:
|
elementary Carathéodory functions |
| MSC:
|
06E15 |
| MSC:
|
06E99 |
| MSC:
|
06F20 |
| MSC:
|
11B99 |
| idZBL:
|
Zbl 0999.06013 |
| idMR:
|
MR1895241 |
| DOI:
|
10.21136/MB.2002.133980 |
| . |
| Date available:
|
2009-09-24T21:57:09Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133980 |
| . |
| Reference:
|
[1] C. Gofman: Remarks on lattice ordered groups and vector lattices, I, Carathéodory functions.Trans. Amer. Math. Soc. 88 (1958), 107–120. MR 0097331 |
| Reference:
|
[2] M. Harminc: Sequential convergences on abelian lattice-ordered groups.Convergence structures, 1984, Math. Research, Band vol. 24, Akademie Verlag, Berlin, 1985, pp. 153–158. Zbl 0581.06009, MR 0835480 |
| Reference:
|
[3] M. Harminc: The cardinality of the system of all sequential convergences on an abelian lattice ordered group.Czechoslovak Math. J. 37 (1987), 533–546. MR 0913986 |
| Reference:
|
[4] J. Jakubík: Cardinal properties of lattice ordered groups.Fundamenta Math. 74 (1972), 85–98. MR 0302528, 10.4064/fm-74-2-85-98 |
| Reference:
|
[5] J. Jakubík: Sequential convergences in Boolean algebras.Czechoslovak Math. J. 38 (1988), 520–530. MR 0950306 |
| Reference:
|
[6] J. Jakubík: Lattice ordered groups having a largest convergence.Czechoslovak Math. J. 39 (1989), 717–729. MR 1018008 |
| Reference:
|
[7] 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:
|
[8] J. Jakubík: Sequential convergences on $MV$-algebras.Czechoslovak Math. J. 45 (1995), 709–726. MR 1354928 |
| Reference:
|
[9] J. Jakubík: Disjoint sequences in Boolean algebras.Math. Bohem. 123 (1998), 411–418. MR 1667113 |
| Reference:
|
[10] H. Löwig: Intrinsic topology and completion of Boolean rings.Ann. Math. 43 (1941), 1138–1196. MR 0006494 |
| Reference:
|
[11] J. Novák, M. Novotný: On the convergence in $\sigma $-algebras of point-sets.Czechoslovak Math. J. 3 (1953), 291–296. |
| Reference:
|
[12] 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 |
| . |
