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Transactions of the American Mathematical Society

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Sequential convergence in the order duals of certain classes of Riesz spaces


Author: P. G. Dodds
Journal: Trans. Amer. Math. Soc. 203 (1975), 391-403
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9947-1975-0358282-0
MathSciNet review: 0358282
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Abstract: Several results of Hahn-Vitali-Saks type are given for sequences in the order dual of an Archimedean Riesz space with separating order dual. The class of Riesz spaces considered contains those which are Dedekind $ \sigma $-complete, or have the projection property or have an interpolation property introduced by G. L. Seever. The results depend on recent work of O. Burkinshaw and some results of uniform boundedness type.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0358282-0
Keywords: Archimedean Riesz spaces, order dual, sequential convergence, principal projection property, weak compactness
Article copyright: © Copyright 1975 American Mathematical Society

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