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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

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)

Citations:

Zbl 0572.00013