Adjective
Not empty, containing something.
(mathematics) Of a set, containing at least one element, thereby being distinct from the empty set.
Source: en.wiktionary.orgA topological space X is disconnected if there exist disjoint, nonempty, closed subsets A and B of X whose union is X. Furthermore, X is totally disconnected if it has an open basis consisting of closed sets. Source: Internet
A partition of a set S is a set of nonempty subsets of S such that every element x in S is in exactly one of these subsets. Source: Internet
A nonempty subset W of a vector space V that is closed under addition and scalar multiplication (and therefore contains the 0-vector of V) is called a linear subspace of V, or simply a subspace of V, when the ambient space is unambiguously a vector space. Source: Internet
Basic properties of subgroups *A subset H of the group G is a subgroup of G if and only if it is nonempty and closed under products and inverses. Source: Internet
Closed sets also give a useful characterization of compactness: a topological space X is compact if and only if every collection of nonempty closed subsets of X with empty intersection admits a finite subcollection with empty intersection. Source: Internet
Comments * The descending chain condition on P is equivalent to P being well-founded : every nonempty subset of P has a minimal element (also called the minimal condition). Source: Internet