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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:
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


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