Generating set
From Freepedia
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.
- If G is a topological space, 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.
