Total set explained

In functional analysis, a total set (also called a complete set) in a vector space is a set of linear functionals

T with the property that if a vector x \in X satisfies f(x) = 0 for all f \in T, then x = 0 is the zero vector.^[1]

In a more general setting, a subset

T of a topological vector space X is a total set or fundamental set if the linear span of T is dense in X. ^[2]

Notes and References

1. Book: Klauder. John R.. A Modern Approach to Functional Integration. limited. 2010. Springer Science & Business Media. 9780817647902. 91.
2. Web site: Lomonosov. L. I.. Total set. Encyclopedia of Mathematics. Springer. 14 September 2014.