Lattice uniformities on effect algebras

Abstract

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations $\ominus$ and $\oplus$ of L are uniquely determined by their system of neighbourhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive $[0,+\infty]$-valued functions on L.