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Descriptions of state spaces of orthomodular lattices (the hypergraph approach)
Mathematica Bohemica, Tome 117 (1992) no. 3, pp. 305-313
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Using the general hypergraph technique developed in [7], we first give a much simpler proof of Shultz's theorem [10]: Each compact convex set is affinely homeomorphic to the state space of an orthomodular lattice. We also present partial solutions to open questions formulated in [10] - we show that not every compact convex set has to be a state space of a unital orthomodular lattice and that for unital orthomodular lattices the state space characterization can be obtained in the context of unital hypergraphs.
Using the general hypergraph technique developed in [7], we first give a much simpler proof of Shultz's theorem [10]: Each compact convex set is affinely homeomorphic to the state space of an orthomodular lattice. We also present partial solutions to open questions formulated in [10] - we show that not every compact convex set has to be a state space of a unital orthomodular lattice and that for unital orthomodular lattices the state space characterization can be obtained in the context of unital hypergraphs.
DOI : 10.21136/MB.1992.126280
Classification : 03G12, 05C65, 06C15
Keywords: affine homeomorphism; compact convex set; hypergraph; unital orthomodular lattices; state space representation; orthomodular lattice; state space 
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Navara, Mirko. Descriptions of state spaces of orthomodular lattices (the hypergraph approach). Mathematica Bohemica, Tome 117 (1992) no. 3, pp. 305-313. doi: 10.21136/MB.1992.126280

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