Almost 𝜎-Dedekind complete Riesz spaces and the main inclusion theorem

Aliprantis, C. D.; Langford, Eric

doi:10.1090/S0002-9939-1974-0346475-2

Almost $\sigma$-Dedekind complete Riesz spaces and the main inclusion theorem
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by C. D. Aliprantis and Eric Langford PDF

Proc. Amer. Math. Soc. 44 (1974), 421-426 Request permission

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.

References

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