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Keywords:
affine homeomorphism; compact convex set; hypergraph; unital orthomodular lattices; state space representation; orthomodular lattice; state space
affine homeomorphism; compact convex set; hypergraph; unital orthomodular lattices; state space representation; orthomodular lattice; state space
Summary:
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.
References:
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