MATHEMATICA BOHEMICA, Vol. 125, No. 2, pp. 139-144 (2000)

Nearly disjoint sequences in convergence $\ell$-groups

Jan Jakubik

Jan Jakubik, Matematicky ustav SAV, Gresakova 6, 040 01 Kosice, Slovakia, e-mail:

Abstract: 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 $\conv G$.

Keywords: convergence $\ell$-group, nearly disjoint sequence, strong convergence

Classification (MSC2000): 06F20, 22C05

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