Lattice uniformities and modular functions on orthomodular lattices
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- Weber, H. Order (1995) 12: 295. doi:10.1007/BF01111744
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It is shown that the lattice of all exhaustive lattice uniformities on an orthomodular latticeL is isomorphic to the centre of a natural completion (of a quotient) ofL, and is thus a complete Boolean algebra. This is applied to prove a decomposition theorem for exhaustive modular functions on orthomodular lattices, which generalizes Traynor's decomposition theorem .