Total set

This article is about a concept in functional analysis. For the type of metric space, see Complete space.

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

• Kadec norm – All infinite-dimensional, separable Banach spaces are homeomorphicPages displaying short descriptions of redirect targets
• Degenerate bilinear form – Concept in linear algebra
• Dual system – Dual pair of vector spaces