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Nearly disjoint sequences in convergence $$\ell$$-groups. (English) Zbl 0967.06013
Summary: For an abelian lattice-ordered group $$G$$ let $$\text{conv} G$$ 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 $$\alpha _{\text{nd}}$$ 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 $$\text{conv} G$$. In the present paper we prove that the join $$\alpha _{\text{nd}}\vee \alpha$$ does exist in $$\text{conv} G$$.

##### MSC:
 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces 22C05 Compact groups
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