Abstract:The set $A$ of all atoms of an atomic orthomodular lattice is said to be almost orthogonal if the set $\{b\in A:b\nleq a'\}$ is finite for every $a\in A$. It is said to be strongly almost orthogonal if, for every $a\in A$, any sequence $b_1, b_2,...$ of atoms such that $a\nleq b'_1, b_1 \nleq b'_2,...$ 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 orthogonal.
Keywords: atomic orthomodular lattice, topological orthomodular lattice, almost orthogonal sets of atoms
AMS Subject Classification: 06C15, 03G12