Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: F^I isomorphic to finite(F^I)
Replies: 11   Last Post: Mar 8, 2013 3:45 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robin Chapman

Posts: 280
Registered: 5/29/08
Re: F^I isomorphic to finite(F^I)
Posted: Mar 6, 2013 6:30 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 05/03/2013 23:03, Kaba wrote:
> Hi,
>
> Let F be a field, and I be a set. Denote by finite(F^I) the set of
> functions from I to F which are non-zero only for finitely many i in I.
>
> Claim
> -----
>
> F^I is isomorphic (as a vector space over F) to finite(F^I) if and only
> if I is finite.
>
> Thoughts
> --------
>
> In addition to the proof, some interesting questions arise:
>
> 1) What is the cardinality of F^I?


|F|^|I| :-)

> 2) What could be a basis for F^I?
>
> 3) What is the dimension of F^I?


Let V be a vector space over the field F. If |V| is infinite and
|V| > |F| then the dimension of V over F is |V|.




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.