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Order convergence in ordered vector spaces: compactness, atoms, pervasiveness, and ice cream spaces

Bilokopytov, Eugene et al.
arXiv (All) · Papers
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functional-analysis
We study order convergence in ordered vector spaces that are not necessarily lattices. In this setting, we consider two generalizations of order convergence on vector lattices, a directed and an undirected variant. We show that these notions agree for the class of pervasive spaces and extend several
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