Boolean algebras of lattice uniformities and decompositions of modular functions

摘要

We study decomposition theorems for modular functions on lattices and the relationship between such decompositions and lattice properties of a suitable system of uniformities. We give a purely topological characterization for the validity of a decomposition theorem of a certain type and examine when this topological condition is satisfied, namely when a system of lattice uniformities is a Boolean algebra consisting of permutable uniformities.