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

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Dr. Eric Wingler

Posts: 139
Registered: 12/12/04
Re: Spans of linear spaces - otre vez
Posted: Mar 15, 2006 1:43 PM
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"Dave Seaman" <dseaman@no.such.host> wrote in message
> On Wed, 15 Mar 2006 07:51:04 -0600, Michael Stemper wrote:
> > In article <130320061442179712%anniel@nym.alias.net.invalid>, A N Niel
> >>In article <200603131914.k2DJEQw105294@walkabout.empros.com>, Michael
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

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