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)


06C15 Complemented lattices, orthocomplemented lattices and posets
06F30 Ordered topological structures
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