Generating set

In mathematics, generating set refers to several related concepts:

• Generating set of a group: S is a generating set of a group if the smallest subgroup of G containing S is G itself.

• Generating set of a ring: S is a generating set of a ring G if the smallest subring of G containing S is G itself??

• If G is a topological group, a subset S of G is said to generate G topologically if the closure of the set generated by S is G. For example, polynomials are a generating set of the space of all continuous functions on the closed unit interval, because taking closure under limits forms the entire space.

• In linear algebra, S is a generating set or spanning set of a vector space V if V is the linear span of S.