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arXiv · 2405.07366

Unbounded order convergence on infinitely distributive lattices

Abela Kevin·Chetcuti Emmanuel
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Abstract

We study uO convergence on infinitely distributive lattices, extending key properties known from Riesz spaces. We show that order continuity of uO convergence characterizes infinite distributivity. We examine O-adherence and uO adherence of sublattices and ideals, proving that the uO and O closures of a sublattice coincide and form a sublattice, and that the first uO adherence of an ideal is an O closed ideal. We also analyze the Dedekind MacNeille completion of a sublattice Y within that of a lattice L, identifying conditions (A) and (B) under which the completion of Y embeds regularly in that of L. In this case, we show that the first uO adherence of Y covers its O closure.

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Abela Kevin, Chetcuti Emmanuel. 2024-05-12. Unbounded order convergence on infinitely distributive lattices. https://arxiv.org/abs/2405.07366

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