## Orthomodular latticesThis book has evolved from a set of lecture notes of a course on orthomodular lattices given at the University of Ulm. Most concepts are developed from their very first notions, but in some instances basic set theory and Hilbert space theory may be needed. The text is in general independent of the exercises and supplementary remarks. The book can be used for a general lecture on orthomodular lattices and also for seminars on special geometrical or logical topics. As the first monograph in the field it makes the widely spread results on orthomodular lattices more easily accessible for researchers. |

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### Contents

Generalities | 13 |

Blocks | 37 |

Closed subspaces of Hilbert space | 64 |

Copyright | |

18 other sections not shown

### Common terms and phrases

Amer Assume assumption astroid automorphism axiomatic Birkhoff blocks Boolean algebra Bruns chain characterization closed subspaces common complement common relative complement commutes complete lattice complete orthomodular lattice Con(L congruence relation contains continuous geometry contradiction countable define definition diagram dimension function dimension lattice dimensional distributive equals equational class equivalence relation example exchange axiom Figure Foulis semigroup Galois connection Greechie Hasse diagram Hence Hilbert space holds homomorphism ideal implies infer infinite irreducible isomorphic Janowitz Lemma Maeda Math maximal modular lattice modular law modular ortholattice obtain operations order ideal order to prove ortho orthocomplementation orthocomplemented orthogonal set orthogonal subset orthomodular law orthomodular poset orthoposet p-ideal pairwise partial order projective geometry Proof Proposition quantum logic quantum mechanics sequence Solution statements are equivalent subalgebra sublattice SUPPLEMENTARY REMARKS supremum symmetric Theorem theory Univ