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- W2899019478 abstract "With each orthomodular lattice L we associate a spectral presheaf $$underline{varSigma }^{L}$$ , generalising the Stone space of a Boolean algebra, and show that (a) the assignment $$Lmapsto underline{varSigma }^{L}$$ is contravariantly functorial, (b) $$underline{varSigma }^{L}$$ is a complete invariant of L, and (c) for complete orthomodular lattices there is a generalisation of Stone representation in the sense that L is mapped into the clopen subobjects of the spectral presheaf $$underline{varSigma }^{L}$$ . The clopen subobjects form a complete bi-Heyting algebra, and by taking suitable equivalence classes of clopen subobjects, one can regain a complete orthomodular lattice isomorphic to L. We interpret our results in the light of quantum logic and in the light of the topos approach to quantum theory." @default.
- W2899019478 created "2018-11-09" @default.
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- W2899019478 date "2018-01-01" @default.
- W2899019478 modified "2023-09-23" @default.
- W2899019478 title "A Generalisation of Stone Duality to Orthomodular Lattices" @default.
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- W2899019478 doi "https://doi.org/10.1007/978-981-13-2487-1_1" @default.
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