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Transactions of the American Mathematical Society

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On the completion of Hausdorff locally solid Riesz spaces


Author: Charalambos D. Aliprantis
Journal: Trans. Amer. Math. Soc. 196 (1974), 105-125
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9947-1974-0350372-0
MathSciNet review: 0350372
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Abstract: In this paper we consider Hausdorff locally solid Riesz spaces $ (L,\tau )$ and we denote by $ (\hat L,\hat \tau )$ the Hausdorff topological completion of $ (L,\tau )$. It is proved that $ (\hat L,\hat \tau )$ is a Hausdorff locally solid Riesz space containing L as a Riesz subspace. We study the properties of $ (L,\tau )$ which are inherited by $ (\hat L,\hat \tau )$.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0350372-0
Keywords: Topological completion, locally solid Riesz spaces, order and topological continuity
Article copyright: © Copyright 1974 American Mathematical Society

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