منابع مشابه
Compact Orthoalgebras
We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove th...
متن کاملTopological Orthoalgebras
We define topological orthoalgebras (TOAs), and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space (in its norm or strong operator topology) is an example of a lattice-ordered TOA that is not a topological lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show tha...
متن کاملGeneralized Ideals in Orthoalgebras
Since in 1936 Birkhoff and von Neumann regarded the lattice of all closed subspaces of a separable infinite-dimensional Hilbert space that is an orthomodular lattice as a proposition system for a quantum mechanical entity (Miklós, 1998), orthomodular lattices have been considered as a mathematical model for a calculus of quantum logic. With the development of the theory of quantum logics, ortho...
متن کاملBoolean Subalgebras of Orthoalgebras
We reconstruct orthoalgebras from their partially ordered set of Boolean subalgebras, and characterize partially ordered sets of this form, using a new notion of a direction. For Boolean algebras, this reconstruction is functorial, and nearly an equivalence.
متن کاملPartition Logics, Orthoalgebras and Automata
We investigate the orthoalgebras of certain non-Boolean models which have a classical realization. Our particular concern will be the partition logics arising from the investigation of the empirical propositional structure of Moore and Mealy type automata.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2005
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-05-07884-6