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Orthomodular lattices with almost orthogonal sets of atoms. (English) Zbl 0762.06003

The set of atoms of an atomic orthomodular lattice is said to be almost orthogonal if for every atom there is only a finite number of atoms not orthogonal to it. It is said to be strongly almost orthogonal if every equivalence class of the transitive closure of the relation of nonorthogonality has a finite number of elements. The authors study the relation between these notions and show some consequences for topological orthomodular lattices.
Reviewer: J.Tkadlec (Praha)

MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets
03G12 Quantum logic
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