"Dave Seaman" <firstname.lastname@example.org> wrote in message news:email@example.com... > On Wed, 15 Mar 2006 07:51:04 -0600, Michael Stemper wrote: > > In article <firstname.lastname@example.org>, A N Niel writes: > >>In article <200603131914.k2DJEQw105294@walkabout.empros.com>, Michael Stemper <email@example.com> wrote:
> > Is there any vector space with an uncountable basis where the basis > > can be demonstrated (FSVO "demonstrated")? > > Let B be any uncountable set and let V be the set of all mappings > f: B -> R. Then V is a vector space and the set of indicator functions > on singleton subsets of B is a basis. >
I think you want the mappings f in V to have the property that f(x) = 0 for all but finitely many x in B. Otherwise, you cannot write f as a finite linear combination of indicator functions on singleton subsets of B.
________________________________ Eric J. Wingler (firstname.lastname@example.org) Dept. of Mathematics and Statistics Youngstown State University One University Plaza Youngstown, OH 44555-0001 330-941-1817