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Nearly disjoint sequences in convergence $l$ -groups

Ján Jakubík (2000)

Mathematica Bohemica

For an abelian lattice ordered group $G$ let $G$ 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 $α_{n d}$ be the convergence on $G$ which is generated by the set of all nearly disjoint sequences in $G$ , and let $α$ be any element of $G$ . In the present paper we prove that the join $α_{n d} \lor α$ does exist in $G$ .