An atom in a poset P with least element 0, is an element that is minimal among all elements that are unequal to 0. An atomic poset P with least element 0 is one in which, for every non-zero element x of P, there is an atom a of P with a ≤ x. Atoms in posets are abstract generalizations of singletons in set theory. Atomicity (the property of being atomic) provides an abstract generalization in the context of order theory of the ability to select an element from a non-empty set.
