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

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: F^I isomorphic to finite(F^I)
Posted: Mar 6, 2013 3:36 PM
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On Wed, 06 Mar 2013 21:34:23 +0200, Kaba <kaba@nowhere.com> wrote:

>6.3.2013 1:47, Shmuel (Seymour J.) Metz wrote:
>> In <kh5tht$csg$1@news.cc.tut.fi>, on 03/06/2013
>> at 01:03 AM, Kaba <kaba@nowhere.com> said:
>>

>>> 2) What could be a basis for F^I?
>>
>>Google for "Hamel Basis".

>
>Sure, a Hamel basis, but is it possible to give some intuitive
>construction for the Hamel basis of F^I?:)


No. If I is infinite there _is_ no "construction" of a basis,
a basis exists by the Axiom of Choice (Zorn's Lemma
gives a maximal independent set).







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