Article

 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 .

Files

Files Size Format View
MathBohem_125-2000-2_3.pdf 1.033Mb application/pdf View/Open

Partner of