total set

{{About|a concept in functional analysis|the type of metric space|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 $x\; \backslash in\; X$ satisfies $f(x)\; =\; 0$ for all $f\; \backslash in\; T,$ then $x\; =\; 0$ is the zero vector.{{cite book|last1=Klauder|first1=John R.|title=A Modern Approach to Functional Integration|url=https://archive.org/details/modernapproachto00jrkl|url-access=limited|date=2010|publisher=Springer Science & Business Media|isbn=9780817647902|page=[https://archive.org/details/modernapproachto00jrkl/page/n107 91]}}

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 $X.${{cite web|last1=Lomonosov|first1=L. I.|title=Total set|url=http://www.encyclopediaofmath.org/index.php?title=Total_set&oldid=14064|website=Encyclopedia of Mathematics|publisher=Springer|accessdate=14 September 2014}}