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Proceedings of the American Mathematical Society

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Almost $ \sigma $-Dedekind complete Riesz spaces and the main inclusion theorem

Authors: C. D. Aliprantis and Eric Langford
Journal: Proc. Amer. Math. Soc. 44 (1974), 421-426
MSC: Primary 46A40
MathSciNet review: 0346475
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Abstract: A Riesz space is almost $ \sigma $-Dedekind complete if it can be embedded as a super order dense Riesz subspace of a $ \sigma $-Dedekind complete space. The location of this concept in the Main Inclusion Theorem of Luxemburg and Zaanen is investigated; it is shown that this concept is implied by $ \sigma $-Dedekind completeness and by the projection property, that it implies the property of being Archimedean, and that it is independent of the principal projection property and the property of having sufficiently many projections.

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Keywords: Almost $ \sigma $-Dedekind complete Riesz spaces, Main Inclusion Theorem, $ \sigma $-Dedekind completion
Article copyright: © Copyright 1974 American Mathematical Society