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arXiv · 2104.13664

The sup-completion of a Dedekind complete vector lattice

Youssef Azouzi·Youssef Nasri
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Abstract

Every Dedekind complete Riesz space X has a unique sup-completion X^{s}, which is a Dedekind complete lattice cone. This paper aims to present a systematic study this cone by extending several known results to general setting, proving new results and, in particular, introducing for elements of X^{s} finite and infinite parts. This enuables us to get a satisfactory abstract formulation of some classical results in the setting of Riesz spaces. We prove, in pareticular, a Riesz space version of Borel-Cantelli Lemma and present some applications to it.29*

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Youssef Azouzi, Youssef Nasri. 2021-04-28. The sup-completion of a Dedekind complete vector lattice. https://arxiv.org/abs/2104.13664

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