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arXiv · 1801.07191

Vector lattice covers of ideals and bands in pre-Riesz spaces

Anke Kalauch·Helena Malinowski
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Abstract

Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover $Y$ for a pre-Riesz space $X$, we address the question how to find vector lattice covers for subspaces of $X$, such as ideals and bands. We provide conditions such that for a directed ideal $I$ in $X$ its smallest extension ideal in $Y$ is a vector lattice cover. We show a criterion for bands in $X$ and their extension bands in $Y$ as well. Moreover, we state properties of ideals and bands in $X$ which are generated by sets, and of their extensions in $Y$.

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Anke Kalauch, Helena Malinowski. 2018-01-22. Vector lattice covers of ideals and bands in pre-Riesz spaces. https://doi.org/10.2989/16073606.2018.1501620

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