Total set

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.

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 $$X.$$