Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2405.07366 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- 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.