| Title:
|
Nearly disjoint sequences in convergence $l$-groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
139-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For an abelian lattice ordered group $G$ let $\conv G$ be the system of all compatible convergences on $G$; this system is a meet semilattice but in general it fails to be a lattice. Let $\alpha_{nd}$ be the convergence on $G$ which is generated by the set of all nearly disjoint sequences in $G$, and let $\alpha$ be any element of $\conv G$. In the present paper we prove that the join $\alpha_{nd}\vee\alpha$ does exist in $\conv G$. (English) |
| Keyword:
|
nearly disjoint sequence |
| Keyword:
|
strong convergence |
| Keyword:
|
convergence $\ell$-group |
| MSC:
|
06F20 |
| MSC:
|
22C05 |
| idZBL:
|
Zbl 0967.06013 |
| idMR:
|
MR1768802 |
| DOI:
|
10.21136/MB.2000.125958 |
| . |
| Date available:
|
2009-09-24T21:41:33Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125958 |
| . |
| Reference:
|
[1] L. Fuchs: Partially Ordered Algebraic Systems.Pergamon Press, Oxford, 1963. Zbl 0137.02001, MR 0171864 |
| Reference:
|
[2] J. Jakubík: Sequential convergences in l-groups without Urysohn's axiom.Czechoslovak Math. J. 42 (1992), 101-116. Zbl 0770.06008, MR 1152174 |
| Reference:
|
[3] J. Jakubík: Disjoint sequences in Boolean algebras.Math. Bohem 123 (1998), 411-418. MR 1667113 |
| Reference:
|
[4] E. P. Shimbireva: On the theory of partially ordered groups.Matem. Sbornik 20 (1947), 145-178. (In Russian.) Zbl 0029.10301, MR 0020558 |
| . |
