The set $A$ of all atoms of an atomic orthomodular lattice is said to be almost ortho\-go\-nal if the set $\{b\in A:b\nleq a'\}$ is finite for every $a\in A$. It is said to be strongly almost ortho\-go\-nal if, for every $a\in A$, any sequence $b_1, b_2,\dots $ of atoms such that $a\nleq b'_1, b_1 \nleq b'_2, \dots $ contains at most finitely many distinct elements. We study the relation and consequences of these notions. We show among others that a complete atomic orthomodular lattice is a compact topological one if and only if the set of all its atoms is almost ortho\-go\-nal.
@article{118422,
author = {Sylvia Pulmannov\'a and Vladim\'\i r Rogalewicz},
title = {Orthomodular lattices with almost orthogonal sets of atoms},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {32},
year = {1991},
pages = {423-429},
zbl = {0762.06003},
mrnumber = {1159789},
language = {en},
url = {http://dml.mathdoc.fr/item/118422}
}
Pulmannová, Sylvia; Rogalewicz, Vladimír. Orthomodular lattices with almost orthogonal sets of atoms. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 423-429. http://gdmltest.u-ga.fr/item/118422/
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