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 Post subject: Vector space
PostPosted: Mon Oct 24, 2016 8:40 pm 
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Joined: Mon Nov 09, 2015 1:52 pm
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Let \(\displaystyle{A}\) be a non-empty set and \(\displaystyle{\mathcal{F}}\) be a non-empty collection

of \(\displaystyle{1-1}\) and onto functions \(\displaystyle{f:A\to \mathbb{R}^n}\) such that : if

\(\displaystyle{f\,,g\in\mathcal{F}}\) then \(\displaystyle{f\circ g^{-1}:\mathbb{R}^n\to \mathbb{R}^n}\)

is \(\displaystyle{\mathbb{R}}\) - linear isomorphism.

Prove that the set \(\displaystyle{A}\) is a vector space (uniquely defined) and each \(\displaystyle{f\in\mathcal{F}}\)

is \(\displaystyle{\mathbb{R}}\) - linear isomorphism.


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