A set of linear functionals on a vector space separating the points of , that is, such that for any non-zero vector there is an with .
A total set in the sense above is also, and more precisely, called a total set of linear functions, [a1].
More generally, a set , where is a topological vector space, is called a total set or fundamental set if the linear span of is dense in . If , the algebraic dual of , is given the weak topology (so that , if is the base field and is an (algebraic) basis for ), the two definitions for a set agree.
|[a1]||S. Rolewicz, "Metric linear spaces" , Reidel (1985) pp. 44|
|[a2]||G. Köthe, "Topological vector spaces" , 1 , Springer (1969) pp. 132, 247ff|
Total set. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Total_set&oldid=14064