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Condition for inducing topology in a vector lattice by the order completion

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Abstract

Properties of an order topology in vector lattices and Boolean algebras are studied. The main result is the following: in a vector lattice or a Boolean algebra with the condition of “closure by one step” (a generalization of the well-known “regularity” property of Boolean algebras and K-spaces) the order topology is induced by the topology of its Dedekind completion. Bibliography: 4 titles.

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References

  1. B. Z. Vulikh,Introduction to the Theory of Partially Ordered Spaces, Groningen (1967).

  2. D. A. Vladimirov,Boolean Algebras [in Russian], Moscow (1969).

  3. A. V. Potepun, “Some forms of convergence in order and topology in partially ordered sets,”Sib. Mat. Zh.,12, No. 4, 819–827 (1971).

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  4. A. V. Potepun, “Order topology in vector lattices with closure by one step,”J. Math. Sci.,80, No. 6, 2328–2332 (1996).

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Translated fromProblemy Matematicheskogo Analiza, No. 16, 1997, pp. 204–207.

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Potepun, A.V. Condition for inducing topology in a vector lattice by the order completion. J Math Sci 92, 4361–4363 (1998). https://doi.org/10.1007/BF02433442

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  • DOI: https://doi.org/10.1007/BF02433442

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