total, functional, analysis, total, also, called, complete, vector, space, linear, functionals, displaystyle, with, property, that, vector, displaystyle, satisfies, displaystyle, displaystyle, then, displaystyle, zero, vector, more, general, setting, subset, d. In functional analysis a total set also called a complete set in a vector space is a set of linear functionals T displaystyle T with the property that if a vector x X displaystyle x in X satisfies f x 0 displaystyle f x 0 for all f T displaystyle f in T then x 0 displaystyle x 0 is the zero vector 1 In a more general setting a subset T displaystyle T of a topological vector space X displaystyle X is a total set or fundamental set if the linear span of T displaystyle T is dense in X displaystyle X 2 See also editKadec norm All infinite dimensional separable Banach spaces are homeomorphicPages displaying short descriptions of redirect targets Degenerate bilinear form Possible x amp y for x E conjugatesPages displaying wikidata descriptions as a fallback Dual system Topologies on spaces of linear mapsReferences edit Klauder John R 2010 A Modern Approach to Functional Integration Springer Science amp Business Media p 91 ISBN 9780817647902 Lomonosov L I Total set Encyclopedia of Mathematics Springer Retrieved 14 September 2014 nbsp This linear algebra related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Total set amp oldid 1108338223, wikipedia, wiki, book, books, library,