Atomic lattice

Summary

A lattice with a least element $0$ is atomic if every nonzero element lies above at least one atom. Every finite lattice is atomic, and so is the lattice of all subsets of a set. The notion separates lattices that are built from minimal pieces from atomless ones such as the interval $[0, 1]$. It is weaker than being atomistic, where every element is a join of atoms.