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
B. Z. Vulikh,Introduction to the Theory of Partially Ordered Spaces, Groningen (1967).
D. A. Vladimirov,Boolean Algebras [in Russian], Moscow (1969).
A. V. Potepun, “Some forms of convergence in order and topology in partially ordered sets,”Sib. Mat. Zh.,12, No. 4, 819–827 (1971).
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