Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Spans of linear spaces - otre vez
Replies: 19   Last Post: Apr 7, 2006 6:42 AM

 Messages: [ Previous | Next ]
 Dr. Eric Wingler Posts: 139 Registered: 12/12/04
Re: Spans of linear spaces - otre vez
Posted: Mar 15, 2006 1:43 PM

"Dave Seaman" <dseaman@no.such.host> wrote in message
news:dv99bm\$g3j\$1@mailhub227.itcs.purdue.edu...
> On Wed, 15 Mar 2006 07:51:04 -0600, Michael Stemper wrote:
> > In article <130320061442179712%anniel@nym.alias.net.invalid>, A N Niel
writes:
Stemper <mstemper@siemens-emis.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 (wingler@math.ysu.edu)
Dept. of Mathematics and Statistics
Youngstown State University
One University Plaza
Youngstown, OH 44555-0001
330-941-1817