Total set

In functional analysis, a total set (also called a complete set) in a vector space is a set of linear functionals T such that if t(s) = 0 for all t in T, then s = 0 is the zero vector.[1]

In a more general setting, a subset T of a topological vector space V is a total set or fundamental set if the linear span of T is dense in V.[2]


  1. ^ Klauder, John R. (2010). A Modern Approach to Functional Integration. Springer Science & Business Media. p. 91. ISBN 9780817647902.
  2. ^ Lomonosov, L. I. "Total set". Encyclopedia of Mathematics. Springer. Retrieved 14 September 2014.