Harminc, Matúš Sequential convergences on Abelian lattice-ordered groups. (English) Zbl 0581.06009 Convergence structures, Proc. Conf., Bechyně/Czech. 1984, Math. Res. 24, 153-158 (1985). [For the entire collection see Zbl 0572.00013.] Author’s summary: ”In the paper the notion of convergence of sequences on abelian lattice-ordered groups is introduced. We investigate order properties of the set \(L_ G\) of all convergences on a given abelian lattice-ordered group G. The set \(L_ G\), equipped with the natural partial order, is shown to be isomorphic to a certain system of subsemigroups of the semigroup \((G^+)^ N\), where \(G^+\) is the positive cone of G. A smallest convergence with a given subset of positive zero sequences is constructed and the construction is used to show that \(L_ G\) need not be a lattice.” Reviewer: B.F.Smarda Cited in 1 ReviewCited in 7 Documents MSC: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 20F60 Ordered groups (group-theoretic aspects) Keywords:convergence of sequences on abelian lattice-ordered groups; convergences; subsemigroups; positive cone Citations:Zbl 0572.00013 PDFBibTeX XML