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Lattice uniformities and modular functions on orthomodular lattices. (English) Zbl 0834.06013
Traynor’s decomposition for group-valued set functions is generalized to exhaustive modular functions. It is shown that the lattice of exhaustive (lattice-) uniformities on an orthomodular lattice $$L$$ is a complete Boolean algebra isomorphic to the centre of a quotient completion of $$L$$.
Reviewer: G.Kalmbach (Ulm)

##### MSC:
 06C15 Complemented lattices, orthocomplemented lattices and posets 06F30 Ordered topological structures (aspects of ordered structures)
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