Geodesic
Nearly disjoint sequences in convergence $l$-groups
Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 139-144

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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 $\conv G$.
DOI : 10.21136/MB.2000.125958
Classification : 06F20, 22C05
Keywords: nearly disjoint sequence; strong convergence; convergence $\ell$-group 
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Jakubík, Ján. Nearly disjoint sequences in convergence $l$-groups. Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 139-144. doi: 10.21136/MB.2000.125958

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