Total set

Edit links
From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by Zhiping Xu (talk | contribs) at 06:57, 16 November 2017 (fix terminalogy error: t(s) is not an inner product). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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]

References

  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.


Stub icon

This linear algebra-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Total_set&oldid=810595902"