In functional analysis, a total set (also called a complete set) in a vector space is a set of linear functionals
with the property that if a vector
satisfies
for all
then
is the zero vector.[1]
In a more general setting, a subset
of a topological vector space
is a total set or fundamental set if the linear span of
is dense in
[2]
See also
References
- ^ Klauder, John R. (2010). A Modern Approach to Functional Integration. Springer Science & Business Media. p. 91. ISBN 9780817647902.
- ^ Lomonosov, L. I. "Total set". Encyclopedia of Mathematics. Springer. Retrieved 14 September 2014.