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# Article

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Keywords:
generalized Boolean algebra; abelian lattice ordered group; sequential convergence; elementary Carathéodory functions
Summary:
In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.
References:
[1] C. Gofman: Remarks on lattice ordered groups and vector lattices, I, Carathéodory functions. Trans. Amer. Math. Soc. 88 (1958), 107–120. MR 0097331
[2] M. Harminc: Sequential convergences on abelian lattice-ordered groups. Convergence structures, 1984, Math. Research, Band vol. 24, Akademie Verlag, Berlin, 1985, pp. 153–158. MR 0835480 | Zbl 0581.06009
[3] M. Harminc: The cardinality of the system of all sequential convergences on an abelian lattice ordered group. Czechoslovak Math. J. 37 (1987), 533–546. MR 0913986
[4] J. Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. DOI 10.4064/fm-74-2-85-98 | MR 0302528
[5] J. Jakubík: Sequential convergences in Boolean algebras. Czechoslovak Math. J. 38 (1988), 520–530. MR 0950306
[6] J. Jakubík: Lattice ordered groups having a largest convergence. Czechoslovak Math. J. 39 (1989), 717–729. MR 1018008
[7] J. Jakubík: Convergences and higher degrees of distributivity of lattice ordered groups and of Boolean algebras. Czechoslovak Math. J. 40 (1990), 453–458. MR 1065024
[8] J. Jakubík: Sequential convergences on $MV$-algebras. Czechoslovak Math. J. 45 (1995), 709–726. MR 1354928
[9] J. Jakubík: Disjoint sequences in Boolean algebras. Math. Bohem. 123 (1998), 411–418. MR 1667113
[10] H. Löwig: Intrinsic topology and completion of Boolean rings. Ann. Math. 43 (1941), 1138–1196. MR 0006494
[11] J. Novák, M. Novotný: On the convergence in $\sigma$-algebras of point-sets. Czechoslovak Math. J. 3 (1953), 291–296.
[12] F. Papangelou: Order convergence and topological completion of commutative lattice-groups. Math. Ann. 155 (1964), 81–107. DOI 10.1007/BF01344076 | MR 0174498 | Zbl 0131.02601

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