## Sequential convergences on Boolean algebras defined by systems of maximal filters.(English)Zbl 0976.54003

Summary: We study sequential convergences defined on a Boolean algebra by systems of maximal filters. We describe the order properties of the system of all such convergences. We introduce the category of 2-generated convergence Boolean algebras and generalize the construction of the Novák sequential envelope to such algebras.

### MSC:

 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54H12 Topological lattices, etc. (topological aspects) 06E15 Stone spaces (Boolean spaces) and related structures 54B30 Categorical methods in general topology
Full Text:

### References:

 [1] R. N. Ball and A. W. Hager: Convergences on archimedean lattice-ordered groups with weak unit. Preprint (19$$\infty$$) · Zbl 0732.06009 [2] G. Birkhoff: Lattices in applied mathematics. Lattice Theory, Proceedings of Symposia in Pure Mathematics, Vol 2, Providence, 1961, pp. 155-184. · Zbl 0101.27201 [3] R. Boerger: Ein allgemeiner Zugang zur Mass- und Integrations-theorie. Habilitationsschrift, Fernuniversität, Hagen. (1989). [4] G. Boole: An Investigation of the Laws of Thought. Walton and Maberly, London, 1854. · Zbl 1205.03003 [5] R. Frič: Sequential structures and probability: categorical reflections. Mathematik-Arbeitspapiere (H.-E. Porst, Universität Bremen, Bremen 48 (1997), 157-169. [6] R. Frič: Rings of maps: convergence and completion. Preprint. · Zbl 0949.54003 [7] R. Frič: A Stone type duality and its applications to probability. Topology Proceedings vol. 22, 1997, pp. 125-137) · Zbl 0945.54012 [8] P. R. Halmos: The foundations of probability. Amer. Math. Monthly 51 (1944), 497-510. · Zbl 0060.28303 [9] H. Herrlich, H. and G. E. Strecker: Category Theory (second edition). Heldermann Verlag, Berlin, 1976. [10] J. Jakubík: Sequential convergences in Boolean algebras. Czechoslovak Math. J. 38 (1988), 520-530. · Zbl 0668.54002 [11] J. Jakubík: Convergences and higher degrees of distributivity of lattice ordered groups and of Boolean algebras. Czechoslovak Math. J. 40 (1990), 453-458. · Zbl 0731.06010 [12] J. Jakubík: Sequential convergences in lattices. Math. Bohem. 117 (1992), 239-258. · Zbl 0763.06002 [13] J. Jakubík: Sequential convergence in distributive lattices. Math. Bohem. 119 (1994), 245-254. · Zbl 0818.06009 [14] J. Jakubík: Sequential convergence in $$MV$$-algebras. Czechoslovak Math. J. 45 (1995), 709-726. · Zbl 0845.06009 [15] J. Jakubík: Disjoint sequences in a Boolean algebra. Math. Bohem. 123 (1998), 411-418. · Zbl 0934.06017 [16] J. Łoś: On the axiomatic treatment of probability. Colloq. Math. 3 (1955), 125-137. · Zbl 0064.12704 [17] J. Łoś: Fields of events and their definition in the axiomatic treatment of probability. Studia Logica 9 (1960), 95-115. · Zbl 0201.49101 [18] J. Novák: Über die eindeutigen stetigen Erweiterungen stetiger Funktionen. Czechoslovak Math. J. 8 (1958), 344-355. · Zbl 0087.37501 [19] J. Novák: On convergence spaces and their seqeuntial envelopes. Czechoslovak Math. J. 15 (1965), 74-100. [20] J. Novák: On sequential envelopes defined by means of certain classes of functions. Czechoslovak Math. J. 18 (1968), 450-456. · Zbl 0164.23401 [21] B. Riečan, B. and T. Neubrunn: Integral, measure, and ordering. Kluwer Academic Publishers, Dordrecht-Boston-London, 1997. [22] R. Sikorski: Boolean algebras (second edition). Springer-Verlag, Berlin, 1964. · Zbl 0123.01303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.