What is Total set?

In functional analysis, a total set in a vector space is a set of linear functionals T {\displaystyle T} with the property that if a vector x ∈ X {\displaystyle x\in X} satisfies f = 0 {\displaystyle f=0} for all f ∈ T , {\displaystyle f\in T,} then x = 0 {\displaystyle x=0} is the zero vector.

In a more general setting, a subset T {\displaystyle T} of a topological vector space X {\displaystyle X} is a total set or fundamental set if the linear span of T {\displaystyle T} is dense in X . {\displaystyle X.}