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 $X.$

See also

• Degenerate bilinear form
• Dual system
• Topologies on spaces of linear maps