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



Kaba
Posts:
289
Registered:
5/23/11


F^I isomorphic to finite(F^I)
Posted:
Mar 5, 2013 6:03 PM


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 nonzero 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?
2) What could be a basis for F^I?
3) What is the dimension of F^I?
 http://kaba.hilvi.org



